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User talk:Ameagle2

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Formal Logic/Predicate Logic/Satisfaction

= Satisfaction =

The rules for assigning truth to sentences of $$\mathcal{L_P}\,\!$$ should say, in effect, that

 * $$\forall \alpha\, \varphi\,\!$$

is true if and only if $$\varphi\,\!$$ is true of every object in the domain. There are two problems. First, $$\varphi\,\!$$ can, in general, have free variables. In particular, $$\alpha\,\!$$ will normally be free (otherwise saying "for all $$\alpha\,\!$$ …" is irrelevant). But formulae with free variables are not sentences and do not have a truth value. Second, we do not yet have a precise way of saying that $$\varphi\,\!$$ is true of every object in the domain. The solution to these problems comes in two parts:

 * assignment of objects from the domain to each of the variables,

 * specification of whether a model satisfies a formula with a particular assignment of variables.

We can then define truth in a model in terms of satisfaction.

Variable assignment
Given model $$\mathfrak{M}\,\!$$, a variable assignment, denoted $$\mathrm{s}\,\!$$, is a function assigning a member of the domain $$|\mathfrak{M}|\,\!$$ to each variable of $$\mathcal{L_P}\,\!$$. For example, if $$|\mathfrak{M}|\,\!$$ contains natural numbers, then $$\mathrm{s}\,\!$$ applied to variable $$x$$ could be $$\mathrm{s}(x) = 7$$.

In addition to variable assignment, we also have the assignment of domain members to constant symbols by the model's interpretation function $$I_{\mathfrak{M}}\,\!$$. Together, we use this information to generate assignments of domain members to arbitrary terms (including, constant symbols, variables, and complex terms formed by operation letters acting on other terms). This is accomplished by an extended variable assignment, denoted $$\overline{\mathrm{s}}\,\!$$, which is defined below. Recall that the interpretation function $$I_{\mathfrak{M}}\,\!$$ assigns semantic values to the operation letters and predicate letters of $$\mathcal{L_P}\,\!$$.

An extended variable assignment $$\overline{\mathrm{s}}\,\!$$ is a function that assigns a value from $$|\mathfrak{M}|\,\!$$ as follows.

 * If $$\alpha\,\!$$ is a variable, then:
 * $$\overline{\mathrm{s}}(\alpha)\ =\ \mathrm{s}(\alpha)\,\!$$

 * If $$\alpha\,\!$$ is a constant symbol (i.e., a 0-place operation letter), then:
 * $$\overline{\mathrm{s}}(\alpha)\ =\ I_{\mathfrak{M}}(\alpha)\,\!$$

 * If $$\zeta\,\!$$ is an n-place operation letter (n greater than 0) and $$\alpha_1,\ \alpha_2,\ \ldots,\ \alpha_n\,\!$$ are terms, then:

 * $$\overline{\mathrm{s}}\big(\,\zeta(\alpha_1,\, \alpha_2,\, \ldots,\, \alpha_n)\,\big)\ = \ I_{\mathfrak{M}}(\zeta)\,\big(\ \overline{\mathrm{s}}(\,\alpha_1),\, \overline{\mathrm{s}}(\alpha_2),\, \ldots,\, \overline{\mathrm{s}}(\alpha_n)\,\big)\,\!$$

Some examples may help. Suppose we have model $$I_{\mathfrak{M}}\,\!$$ where:

 * $$|\mathfrak{M}|\ =\ \{1,\, 2,\, 3\}\ .\,\!$$
 * $$I_{\mathfrak{M}}(a^0_0)\ =\ 0\ .\,\!$$
 * $$I_{\mathfrak{M}}(b^0_0)\ =\ 1\ .\,\!$$
 * $$I_{\mathfrak{M}}(f^2_0)\ =\ \mathfrak{f}^2_0\ \mbox{such that:} \quad \mathfrak{f}^2_0(0,\, 0) = 2,\ \mathfrak{f}^2_0(0,\, 1)\ =\ 1,\ \mathfrak{f}^2_0(0,\, 2) = 0,\,\!$$
 * $$\mathfrak{f}^2_0(1,\, 0) = 1,\ \mathfrak{f}^2_0(1,\, 1)\ =\ 0,\ \mathfrak{f}^2_0(1,\, 2) = 2,\ \mathfrak{f}^2_0(2,\, 0) = 0,\,\!$$
 * $$\mathfrak{f}^2_0(2,\, 1) = 2,\ \mbox{and}\ \mathfrak{f}^2_0(2,\, 2) = 1\ .\,\!$$

On the previous page, it was noted that we want the following result:

 * $$f(a, b)\ \mbox{resolves to}\ 1\ \mathrm{in}\ \mathfrak{M}\ .\,\!$$

We now have achieved this because we have for any $$\mathrm{s}\,\!$$ defined on $$I_{\mathfrak{M}}\,\!$$:

 * $$\overline{\mathrm{s}}(f(a, b))

\ =\ I_{\mathfrak{M}}(f)\,(\ \overline{\mathrm{s}}(a),\, \overline{\mathrm{s}}(b)\ ) \ =\ \mathfrak{f}^2_0(\ \overline{\mathrm{s}}(a),\, \overline{\mathrm{s}}(b)\ )\,\!$$
 * $$=\ \mathfrak{f}^2_0(\ I_{\mathfrak{M}}(a),\, I_{\mathfrak{M}}(b)\ )

\ =\ \mathfrak{f}^2_0(0,\, 1) \ =\ 1\ .\,\!$$

Suppose we also have a variable assignment $$\mathrm{s}\,\!$$ where:

 * $$\mathrm{s}(x_0)\ =\ 0\ .\,\!$$
 * $$\mathrm{s}(y_0)\ =\ 1\ .\,\!$$

Then we get:

 * $$\overline{\mathrm{s}}(f(x, y))

\ =\ I_{\mathfrak{M}}(f)\,(\ \overline{\mathrm{s}}(x),\, \overline{\mathrm{s}}(y)\ ) \ =\ \mathfrak{f}^2_0(\ \overline{\mathrm{s}}(x),\, \overline{\mathrm{s}}(y)\ )\,\!$$
 * $$=\ \mathfrak{f}^2_0(f)\,(\ \mathrm{s}(x),\, \mathrm{s}(y)\ )

\ =\ \mathfrak{f}^2_0(0,\, 1) \ =\ 1\ .\,\!$$

Satisfaction
A model, together with a variable assignment, can satisfy (or fail to satisfy) a formula. Then we will use the notion of satisfaction with a variable assignment to define truth of a sentence in a model. We can use the following convenient notation to say that the interpretation $$\mathfrak{M}\,\!$$ satisfies (or does not satisfy) $$\varphi\,\!$$ with $$\mathrm{s}\,\!$$.

 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \varphi\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash\, \varphi\,\!$$

We now define satisfaction of a formula by a model with a variable assignment. In the following, 'iff' is used to mean 'if and only if'.

 * $$\mbox{i.} \quad \mbox{For}\ \sigma\ \mbox{a sentence letter:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \sigma \quad \mbox{iff} \quad I_{\mathfrak{M}}(\sigma)\ =\ \mathrm{True}\ .\,\!$$

 * $$\mbox{ii.} \quad \mbox{For}\ \pi\ \mbox{an}\ n\mbox{--place predicate letter and for}\ \alpha_0,\, \alpha_1,\, \ldots,\, \alpha_n\ \mbox{any terms:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \pi(\alpha_0,\, \alpha_1,\, \ldots,\, \alpha_n) \quad \mbox{iff} \ \langle\overline{\mathrm{s}}(\alpha_0),\, \overline{\mathrm{s}}(\alpha_1),\, \ldots,\, \overline{\mathrm{s}}(\alpha_n)\rangle\ \in\ I_{\mathfrak{M}}(\pi)\ .\,\!$$

 * $$\mbox{iii.} \quad \mbox{For}\ \varphi\ \mbox{a formula:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \lnot \varphi \quad \mbox{iff} \ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \varphi\ .\,\!$$

 * $$\mbox{iv.} \quad \mbox{For}\ \varphi\ \mbox{and}\ \psi\ \mbox{formulae:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash (\varphi \land \psi) \quad \mbox{iff} \ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \varphi\ \ \mbox{and}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \psi\ .\,\!$$

 * $$\mbox{v.} \quad \mbox{For}\ \varphi\ \mbox{and}\ \psi\ \mbox{formulae:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash (\varphi \lor \psi) \quad \mbox{iff} \ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \varphi\ \ \mbox{or}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \psi\ \mbox{(or both)}\ .\,\!$$

 * $$\mbox{vi.} \quad \mbox{For}\ \varphi\ \mbox{and}\ \psi\ \mbox{formulae:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash (\varphi \rightarrow \psi) \quad \mbox{iff} \ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \varphi\ \ \mbox{or}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \psi\ \mbox{(or both)}\ .\,\!$$

 * $$\mbox{vii.} \quad \mbox{For}\ \varphi\ \mbox{and}\ \psi\ \mbox{formulae:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash (\varphi \leftrightarrow \psi) \quad \mbox{iff} \ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash (\varphi \land \psi)\ \ \mbox{or}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash (\lnot \varphi \land \lnot \psi)\ \mbox{(or both)}\ .\,\!$$

 * $$\mbox{viii.} \quad \mbox{For}\ \varphi\ \mbox{a formula and}\ \alpha\ \mbox{a variable:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \forall \alpha\, \varphi \quad \mbox{iff}\ \ \mbox{for every}\ \mathrm{d}\ \in |\mathfrak{M}|, \ \langle\mathfrak{M},\ \mathrm{s[\alpha\!:\, d]}\rangle\ \vDash \varphi\ .\,\!$$
 * $$\mbox{where}\ \mathrm{s[\alpha\!:\, d]}\ \mbox{differs from}\ \mathrm{s}\ \mbox{only in assigning}\ \mathrm{d}\ \mbox{to}\ \alpha\ .\,\!$$.

 * $$\mbox{ix.} \quad \mbox{For}\ \varphi\ \mbox{a formula and}\ \alpha\ \mbox{a variable:}\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \exists \alpha\, \varphi \quad \mbox{iff}\ \ \mbox{for at least one}\ \mathrm{d} \in |\mathfrak{M}|, \ \langle\mathfrak{M},\ \mathrm{s[\alpha\!:\, d]}\rangle\ \vDash \varphi\ .\,\!$$
 * $$\mbox{where}\ \mathrm{s[\alpha\!:\, d]}\ \mbox{differs from}\ \mathrm{s}\ \mbox{only in assigning}\ \mathrm{d}\ \mbox{to}\ \alpha\ .\,\!$$.

Examples
The following continue the examples used when describing extended variable assignments above. They are based on the examples of the previous page.

A model and variable assignment for examples
Suppose we have model $$I_{\mathfrak{M}}\,\!$$ where

 * $$|\mathfrak{M}|\ =\ \{0,\, 1,\, 2\}\ .\,\!$$
 * $$I_{\mathfrak{M}}(a^0_0)\ =\ 0\ .\,\!$$
 * $$I_{\mathfrak{M}}(b^0_0)\ =\ 1\ .\,\!$$
 * $$I_{\mathfrak{M}}(c^0_0)\ =\ 2\ .\,\!$$
 * $$I_{\mathfrak{M}}(f^2_0)\ =\ \mathfrak{f}^2_0\ \mbox{such that:} \quad \mathfrak{f}^2_0(0,\, 0) = 2,\ \mathfrak{f}^2_0(0,\, 1)\ =\ 1,\ \mathfrak{f}^2_0(0,\, 2) = 0,\,\!$$
 * $$\mathfrak{f}^2_0(1,\, 0) = 1,\ \mathfrak{f}^2_0(1,\, 1)\ =\ 0,\ \mathfrak{f}^2_0(1,\, 2) = 2,\ \mathfrak{f}^2_0(2,\, 0) = 0,\,\!$$
 * $$\mathfrak{f}^2_0(2,\, 1) = 2,\ \mbox{and}\ \mathfrak{f}^2_0(2,\, 2) = 1\ .\,\!$$
 * $$I_{\mathfrak{M}}(\mathrm{F^2_0})\ =\ \{\langle0,\ 1\rangle,\ \langle1,\ 2\rangle,\ \langle2,\ 1\rangle\}\ .\,\!$$

Suppose further we have a variable assignment $$\mathrm{s}\,\!$$ where:

 * $$\mathrm{s}(x_0)\ =\ 0\ .\,\!$$
 * $$\mathrm{s}(y_0)\ =\ 1\ .\,\!$$
 * $$\mathrm{s}(z_0)\ =\ 2\ .\,\!$$

We already saw that both of the following resolve to 1:

 * $$f(a, b)\,\!$$
 * $$f(x, y)\,\!$$

Examples without quantifiers
Given model $$\mathfrak{M}\,\!$$, the previous page noted the following further goals:

 * $$(1) \quad \mathrm{F}(a, b),\ \mathrm{F}(b, c),\ \mbox{and}\ \mathrm{F}(c, b)\ \mbox{are True in}\ \mathfrak{M}\ .\,\!$$
 * $$(2) \quad \mathrm{F}(a, a)\ \mbox{is False in}\ \mathfrak{M}\ .\,\!$$
 * $$(3) \quad \mathrm{F}(a, f(a, b))\ \mbox{is True in}\ \mathfrak{M}\ .\,\!$$
 * $$(4) \quad \mathrm{F}(f(a, b), a)\ \mbox{is False in}\ \mathfrak{M}\ .\,\!$$
 * $$(5) \quad \mathrm{F}(c, b) \rightarrow \mathrm{F}(a, b)\ \mbox{is True in}\ \mathfrak{M}\ .\,\!$$
 * $$(6) \quad \mathrm{F}(c, b) \rightarrow \mathrm{F}(b, a)\ \mbox{is False in}\ \mathfrak{M}\ .\,\!$$

We are not yet ready to evaluate for truth or falsity, but we can take a step in that direction by seeing that these sentences are satisfied by $$\mathfrak{M}\,\!$$ with $$\mathrm{s}.\,\!$$ Indeed, the details of $$\mathrm{s}\,\!$$ will not figure in determining which of these are satisfied. Thus $$\mathfrak{M}\,\!$$ satisfies (or fails to satisfy) them with any variable assignment. As we will see on the next page, that is the criterion for truth (or falsity) in $$\mathfrak{M}\,\!$$.

Corresponding to (1),

 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(a, b),\ \mathrm{F}(b, c),\ \mbox{and}\ \mathrm{F}(c, b)\ .\,\!$$

In particular:

 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(a, b)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(a),\, \overline{\mathrm{s}}(b)\rangle\ =\ \langle0,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(b, c)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(b),\, \overline{\mathrm{s}}(c)\rangle\ =\ \langle1,\, 2\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(c, b)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(c),\, \overline{\mathrm{s}}(b)\rangle\ =\ \langle2,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$

Corresponding to (2) through (6) respectively:

 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(a, a))\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(a),\, \overline{\mathrm{s}}(a)\rangle\ =\ \langle0,\, 0\rangle\ \notin\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(a, f(a, b))\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(a),\, \overline{\mathrm{s}}(f(a, b))\rangle\ =\ \langle0,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(f(a, b), a)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(f(a, b),\, \overline{\mathrm{s}}(a)\rangle\ =\ \langle1,\, 0\rangle\ \notin\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(c, b) \rightarrow \mathrm{F}(a, b)\ \ \mbox{because}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(a, b)\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(c, b) \rightarrow \mathrm{F}(b, a)\ \ \mbox{because}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(c, b)\ \mbox{but}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(b, a)\ .\,\!$$

As noted above, the details of $$\mathrm{s}\,\!$$ were not relevant to these evaluations. But for similar formulae using free variables instead of constant symbols, the details or $$\mathrm{s}\,\!$$ do become relevant. Examples based the above are:

 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(x, y)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(x),\, \overline{\mathrm{s}}(y)\rangle\ =\ \langle0,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(y, z)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(y),\, \overline{\mathrm{s}}(z)\rangle\ =\ \langle1,\, 2\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(z, y)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(z),\, \overline{\mathrm{s}}(y)\rangle\ =\ \langle2,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(x, x))\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(x),\, \overline{\mathrm{s}}(x)\rangle\ =\ \langle0,\, 0\rangle\ \notin\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(x, f(x, y))\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(x),\, \overline{\mathrm{s}}(f(x, y))\rangle\ =\ \langle0,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(f(x, y), x)\ \ \mbox{because}\ \langle\overline{\mathrm{s}}(f(x, y),\, \overline{\mathrm{s}}(x)\rangle\ =\ \langle1,\, 0\rangle\ \notin\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(z, y) \rightarrow \mathrm{F}(x, y)\ \ \mbox{because}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(x, y)\ .\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(z, y) \rightarrow \mathrm{F}(y, x)\ \ \mbox{because}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \mathrm{F}(z, y)\ \mbox{but}\ \langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \mathrm{F}(y, x)\ .\,\!$$

Examples with quantifiers
Given model $$\mathfrak{M}\,\!$$, the previous page also noted the following further goals:

 * $$(7) \quad \forall x\, \forall y\, (\mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x))\ \mbox{is false in }\ \mathfrak{M}\ .\,\!$$

 * $$(8) \quad \exists x\, \exists y\, (\mathrm{F}(x, y) \land \mathrm{F}(y, x))\ \mbox{is true in}\ \mathfrak{M}\ .\,\!$$

Again, we are not yet ready to evaluate for truth or falsity, but again we can take a step in that direction by seeing that the sentence in (7) is and the sentence in (8) is not satisfied by $$\mathfrak{M}\,\!$$ with $$\mathrm{s}.\,\!$$

Corresponding to (7):

 * $$(9) \quad \langle\mathfrak{M},\ \mathrm{s}\rangle\ \not\vDash \forall x\, \forall y\, (\mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x))\,\!$$

is true if and only if at least one of the following is true:

 * $$(10) \quad \langle\mathfrak{M},\ \mathrm{s}[x\!:\, 0]\rangle\ \not\vDash \forall y\, (\mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x))\,\!$$
 * $$(11) \quad \langle\mathfrak{M},\ \mathrm{s}[x\!:\, 1]\rangle\ \not\vDash \forall y\, (\mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x))\,\!$$
 * $$(12) \quad \langle\mathfrak{M},\ \mathrm{s}[x\!:\, 2]\rangle\ \not\vDash \forall y\, (\mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x))\,\!$$

The formula of (7) and (9) is satisfied by $$\langle\mathfrak{M},\ \mathrm{s}\rangle\,\!$$ if and only if it is satisfied by $$\mathfrak{M}\,\!$$ with each of the modified variable assignments. Turn this around, and we get the formula failing to be satisfied by $$\langle\mathfrak{M},\ \mathrm{s}\rangle\,\!$$ if and only if it fails to be satisfied by the model with at least one of the three modified variable assignments as per (10) through (12). Similarly, (10) is true if and only if at least one of the following are true:

 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 0,\ y\!:\, 0]\rangle\ \not\vDash \mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x)\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 0,\ y\!:\, 1]\rangle\ \not\vDash \mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x)\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 0,\ y\!:\, 2]\rangle\ \not\vDash \mathrm{F}(x, y) \rightarrow \mathrm{F}(y, x)\,\!$$

Indeed, the middle one of these is true. This is because

 * $$\langle0,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ \mbox{but}\, \langle1,\, 0\rangle\ \not\in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$

Thus (9) is true.

Corresponding to (8),

 * $$(13) \quad \langle\mathfrak{M},\ \mathrm{s}\rangle\ \vDash \exists x\, \exists y\, (\mathrm{F}(x, y) \land \mathrm{F}(y, x))\,\!$$

is true if and only if at least one of the following is true:

 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 0]\rangle\ \vDash \exists y\, (\mathrm{F}(x, y) \land \mathrm{F}(y, x))\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 1]\rangle\ \vDash \exists y\, (\mathrm{F}(x, y) \land \mathrm{F}(y, x))\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 2]\rangle\ \vDash \exists y\, (\mathrm{F}(x, y) \land \mathrm{F}(y, x))\,\!$$

The middle of these is true if and only if at least one of the following are true:

 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 1,\ y\!:\, 0]\rangle\ \vDash \mathrm{F}(x, y) \land \mathrm{F}(y, x)\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 1,\ y\!:\, 1]\rangle\ \vDash \mathrm{F}(x, y) \land \mathrm{F}(y, x)\,\!$$
 * $$\langle\mathfrak{M},\ \mathrm{s}[x\!:\, 1,\ y\!:\, 2]\rangle\ \vDash \mathrm{F}(x, y) \land \mathrm{F}(y, x)\,\!$$

Indeed, the last of these is true. This is because:

 * $$\langle1,\, 2\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ \mbox{and}\, \langle2,\, 1\rangle\ \in\ I_{\mathfrak{M}}(\mathrm{F})\ .\,\!$$

Thus (13) is true.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Blender 3D: Noob to Pro/Rendering Information

Only some links to wikipedia articles for now

 * Rendering (computer graphics)

 * Specular reflection
 * Diffuse reflection

 * Flat shading
 * Gouraud shading
 * Phong shading

 * Lambertian diffuse lighting model
 * Phong reflection model


text:
Template:Booleq

vi:Tiêu bản:Booleq

title: Template:Booleq


text:
Template:Booleq/eq2

vi:Tiêu bản:Booleq/eq2

title: Template:Booleq/eq2


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Cookbook:Anise Bread (Penia)

Penia is a sweet bread of Italian origin traditionally made at Easter time.

Procedure

 * 1) Dissolve the yeast cakes in the warm water and set aside.
 * 2) Beat eggs until fluffy.
 * 3) Add sugar and beat.
 * 4) Add melted butter and beat, then add salt.
 * 5) Add the juices and spices.
 * 6) Add the water-yeast mixture, and stir until well blended.
 * 7) Add flour, then mix until ready for kneading.
 * 8) Knead thoroughly until dough springs back when finger-poked.
 * 9) Allow dough to rise overnight (12 hours) or until doubled in size.
 * 10) Divide dough into 7 portions.
 * 11) Shape each portion into the shape of dolls.
 * 12) Allow to rise for 2 to 3 hours.
 * 13) Bake at 275–300°F (140–160°C) for 15–20 minutes.

Notes, tips, and variations

 * Yeast cakes seem to work better than dry yeast. But, you can use 2 packs of dried yeast instead of the yeast cakes.
 * You can use 1 tbsp (13 g) lemon extract instead of the lemon juice.
 * Alternately it is shaped into a couple of large rings with shell-on hard boiled eggs embedded in the dough at the cardinal points. The eggs were a symbol of resurrection and the four directions the sign of the cross.
 * Don't forget the sweet glaze; 1lb (450g) of confectioners' sugar with enough water to make it spreadable. Spread on each loaf and cover generously with colorful sprinkles!

title: Cookbook:Anise Bread (Penia)


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Orthopaedic Surgery/Motor Vehicle Accidents

Motor Vehicle Accidents

It seems driving a car is ease to learn and difficult to master. In fact the environment of a modern automobile with emphasis on comfort and quiet smooth ride and with numerous opportunities for quelling what is usually a tedious experience of careening along a well constructed modern highway at high speed. Inattention then to the potential hazard close at hand which can result from the rapid unexpected deceleration of the vehicle in the face of a collision. Safety improvements have also accompanied the evolution of the automobile to be sure beginning with seat belts then air  bags and evolving toward collision warning and driver consciousness monitoring, perhaps including measures to prevent a drunk from becoming a drunk driver. Some of these advances may make serious collisions more survivable thus increasing the volume of high energy extremity fractures to be treated. Regulation of driving with speed limits and video surveillance and public awareness measures pointing out the statistical relatedness of young drivers accidents and distractions, number of passengers, radio, eating cell phones, night driving. Legislation pits interest groups in ways which lead to compromise which do not always lead to a priority on safety but rather a balance of safety and commerce. Even the evolution of community planning which may lessen commuting negate the motivation for larger vehicles which offer some protection but more of a false sense of security and in some cases longer break time, and inferior collision avoidance capability. Roads and communities that do not pit drivers against heavy truck traffic may offer solutions.

While we wait for these social and technological advances we contend with injuries sustained from motor vehicle related trauma on our highways. We continue to develop new ways to meet our need for speed in our recreational activities, through ATV's, snowmobiles, personal watercraft and aircraft. The issues are largely the same from an orthopedic standpoint once a living victim has arrived at the emergency department. Injury prevention issues surrounding technological advances and regulation sometimes fueled by litigation continue to change our habits balancing our desires for safety and thrill.

Speed limits.

The issue of maximum speed limits is controversial. The argument in favor of a 55 mile per hour limit was based of safety. Today the same safety argument can lead to increasing the allowed speed limit when it is recognized that the ambient rate of speed is well in excess of the posted limit fewer accidents may occur by increasing the speed limit. This approach would seem to reflect a more nuanced understanding of driving habit. There are drivers who observe the posted limit no matter what, and then there are drivers who drive at what they believe to be a safe speed, when the posted limit seems too slow. This second category can be distinguished from a group that routinely drives at a reckless rate of speed well above the posted limit and in fact, well in excess of the ambient flow of traffic. The lowest rate of accidents may be achieved by matching the limit to what a reasonable driver is likely to feel is a safe rate of travel for a given road.

Driving Age.

The rite of passage we associate with the coming of age 16 is being reconsidered in view of statistics recognizing automotive deaths as the leading cause of death among 16 to 20 year olds accounting for twice the fatalities of the next category which is homicide according to the National Highway Traffic Safety Administration.

Over the last 10 years there has been a 12% drop in the licensure rates of 16 year olds such that presently 30% of 16 year olds hold licenses. This trend has accompanied a 26% drop in fatalities, in 16 year old drivers and their passengers. The costs of insuring a 16 year old may be partly motivating this trend as adding a 16 year old to a policy will generally double the premium, and when they are the primary driver of the vehicle, it triples the premium.


text:
Orthopaedic Surgery/Interpersonal Violence

Interpersonal violence

Understanding the social context of our patients with trauma can only help us deliver effective care. Interpersonal violence is seemingly a legacy of our evolution as it is prevalent in chimpanzees and in neanderthal remains. Patterns of interpersonal violence seem to be set early in life and relate in all cases to concern for social status, thus stratification within society with regard to economic and social privilege.

The natural man has only two primal passions, to get and to beget. William Osler

With this quote in mind we consider the thinking of Edward O. Wilson (EdwinWilson) who points out that our planet will be reaching what may be a Malthusian limit of 8 billion individuals within the next two decades. It will increasingly be the tendency for all to want the overconsumption of resources that we in the western enclave have come to expect. In view of these facts we can expect that interpersonal violence with increasing sophistication will continue to evolve, terrorism being its most dramatic manifestation; interpersonal violence writ large. http://www.annalsnyas.org/cgi/content/abstract/1036/1/1?maxtoshow=&HITS=&hits=&RESULTFORMAT=1&andorexacttitle=and&fulltext=why&andorexactfulltext=or&searchid=1&FIRSTINDEX=20&sortspec=relevance&resourcetype=HWCIT

http://www.annalsnyas.org/cgi/content/abstract/1036/1/47?maxtoshow=&HITS=&hits=&RESULTFORMAT=&fulltext=violence+and+inequality&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&resourcetype=HWCIT

http://www.pnas.org/cgi/content/full/99/9/6444?maxtoshow=&HITS=&hits=&RESULTFORMAT=&fulltext=interpersonal+violence+and+society&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&resourcetype=HWCIT

http://www.annalsnyas.org/cgi/content/abstract/1036/1/233?maxtoshow=&HITS=&hits=&RESULTFORMAT=&fulltext=interpersonal+violence+and+society&andorexactfulltext=and&searchid=1&FIRSTINDEX=10&resourcetype=HWCIT

http://jama.ama-assn.org/cgi/content/abstract/282/5/447?maxtoshow=&HITS=&hits=&RESULTFORMAT=&fulltext=cost+of+medical+documentation&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&resourcetype=HWCIT

Society begins with the desire for personal security derived from association with a group. Efficiencies are gained such that the individual is free to function productively without the burden of attending to their personal security and that of their family, at least under ideal circumstances.

A collective defense in the form of a military and police establishes an effective monopoly on purposeful violence. The power of this need to live free of the fear of random violence means a willingness at times to accept the potential for a tyrrany imposed by the government. While no system of government is fail safe in this regard, system of government must include provision for the will of the people to be made known and for the mantle of authority to change hands in a peaceful and orderly fashion that reflects that will. Where that right is abridged one can expect the eventual degradation of the government, individual and collective violence against the government which appears to be imposing a tyrrany. Our own government employes a system of checks and balances dividing power between coequal branches

The practice of a collective effort for mutual protection then provides template for  all other collective efforts yielding the bulk of what we have come to enjoy as the accoutrements of life in modern society. Little can be achieved by an individual acting alone without the direct or indirect support of others. The shared interests of the group which function in a coordinated fashion towards a mutually agreed end it thereby actuated.

Research in the area of cognitive neuroscience is leading to a greater understanding of the neurological mechanisms that are the underpinnings of our sense of justice and morality. It seems that some aspects are innate and others a function of socialization. Most of our thoughts in a given day are indeed devoted to contemplating interactions with our fellow humans, either retrospectively or prospectively, so our thinking mechanisms are largely employed most of the time towards the analysis or at least contemplation of such matters.

http://www.sciencemag.org/cgi/content/summary/306/5695/373?maxtoshow=&HITS=&hits=&RESULTFORMAT=1&andorexacttitle=and&fulltext=cognitive+neuroscience+and+the+law&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&sortspec=relevance&resourcetype=HWCIT

http://www.sciencemag.org/cgi/content/abstract/293/5537/2105?maxtoshow=&HITS=&hits=&RESULTFORMAT=1&andorexacttitle=and&fulltext=cognitive+neuroscience+and+the+law&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&sortspec=relevance&resourcetype=HWCIT

http://www.loc.gov/catdir/toc/ecip053/2004026860.html

http://jnnp.bmjjournals.com/cgi/content/full/71/6/727?maxtoshow=&HITS=&hits=&RESULTFORMAT=&fulltext=pack+hierarchy+and+violence&andorexactfulltext=and&searchid=1&FIRSTINDEX=10&resourcetype=HWCIT


text:
Occupational Health/Occupational Injury

As individuals in a modern society we leave the protection of our homes, and travel to our jobs to engage in a collective enterprise which serves the dual purpose of fulfilling our own needs for an income and the needs of our employer for an income and the needs of society for the product or service that our efforts contribute toward. It is a reasonable bargain in most cases and thus we leave the safety and comfort of our homes willingly, though at times not happily, but in any case with every expectation of returning to the safety and comfort of our homes at the end of the day essentially intact.

Occupational safety is the shared interest of worker, employer and government. There is an inherent compromise that is struck between safety and productivity as these are inevitably in conflict. Ultimately however the loss of productivity associated with an injured of killed worker and the loss of a productive member of society makes worker safety our common goal even if we ignore all human compassion that would find no economic justification worth the price of a severely injured extremity of worker demise.

The provision for a safe working environment requires the linking of responsibility for an injury to the worker and the employer alike. It is reasonable to expect that a worker will engage in a given activity in a sensible fashion and with all faculties in place, and with a compliant attitude toward behaviorly linked safety measures that have been inculcated by the policies of the employer. Piece work driven industrial processes are most likely to amplify the risks to workers as they work harder and faster and with any shortcut they may perceive in order to maximize their gain for time expended.

Salaried employment with an expected benchmark quota will enforce a level of productivity which will be geared to a minimum standard which can be achieved by a worker.

The linkage of responsibility for injury to a worker to his employer is justified by the fact that the participation in the work setting is a proximate cause of the injury sustained and that factors in the work environment unrelated to the workers behavior result in the injury. Litigation becomes the default result of dispute over responsibility and threatens by virtue of the shear volume of litigation that could potentially result. As a consequence we evolve systems of regulation for worker safety that are intended to enforce an acceptable level of safety thereby minimizing the risks to an acceptable level and in any case precluding the possibility of economic gain through a disregard for worker safety through an enforced sanctioning of the enterprise by the responsible government agency. Secondly we have evolved a system of workers compensation whereby an agreed system of compensation which includes allowance for lost time, medical expenditure, impairment and vocational rehabilitation where necessary.

title: Occupational Health/Occupational Injury


text:
Orthopaedic Surgery/Occupational Injury

Occupational Injury

As individuals in a modern society we leave the protection of our homes, and travel to our jobs to engage in a collective enterprise which serves the dual purpose of fulfilling our own needs for an income and the needs of our employer for an income and the needs of society for the product or service that our efforts contribute toward. It is a reasonable bargain in most cases and thus we leave the safety and comfort of our homes willingly, though at times not happily, but in any case with every expectation of returning to the safety and comfort of our homes at the end of the day essentially intact.

Occupational safety is the shared interest of worker, employer and government. There is an inherent compromise that is struck between safety and productivity as these are inevitably in conflict. Ultimately however the loss of productivity associated with an injured of killed worker and the loss of a productive member of society makes worker safety our common goal even if we ignore all human compassion that would find no economic justification worth the price of a severely injured extremity of worker demise.

The provision for a safe working environment requires the linking of responsibility for an injury to the worker and the employer alike. It is reasonable to expect that a worker will engage in a given activity in a sensible fashion and with all faculties in place, and with a compliant attitude toward behaviorly linked safety measures that have been inculcated by the policies of the employer. Piece work driven industrial processes are most likely to amplify the risks to workers as they work harder and faster and with any shortcut they may perceive in order to maximize their gain for time expended.

Salaried employment with an expected benchmark quota will enforce a level of productivity which will be geared to a minimum standard which can be achieved by a worker.

The linkage of responsibility for injury to a worker to his employer is justified by the fact that the participation in the work setting is a proximate cause of the injury sustained and that factors in the work environment unrelated to the workers behavior result in the injury. Litigation becomes the default result of dispute over responsibility and threatens by virtue of the shear volume of litigation that could potentially result. As a consequence we evolve systems of regulation for worker safety that are intended to enforce an acceptable level of safety thereby minimizing the risks to an acceptable level and in any case precluding the possibility of economic gain through a disregard for worker safety through an enforced sanctioning of the enterprise by the responsible government agency. Secondly we have evolved a system of workers compensation whereby an agreed system of compensation which includes allowance for lost time, medical expenditure, impairment and vocational rehabilitation where necessary.

title: Orthopaedic Surgery/Occupational Injury


text:
Talk:PHP Programming/Sessions

Under Using Sessions, the first example of registering a session name (second code box) uses session_register("example"); Shouldn't this be session_register($example); I'm new to PHP (which is why I'm reading the guide, of course), but it seems as though keeping it how it's printed would set the session name to "example," not "Test."

(of course it goes on to say that session_register is deprecated, so this suddenly becomes a moot point)

--Sigafoos

A quick visit to http://nl3.php.net/session_register learns us that the parameter for session_register should be a string and not a (as what i suspect you mean) reference to a variable.

so in short: it should be session_register("example");

title: Talk:PHP Programming/Sessions


text:
User talk:Super Dave~enwikibooks

 * Hello my name is David N B.

I created a Wikibook account because I wanted to help improve on the Wikibook Blender 3D: Noob to Pro.

While also learning to become a Pro instead of a Noob at Blender 3D

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Super Dave. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Super Dave~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:44, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:34, 19 April 2015 (UTC)

title: User talk:Super Dave~enwikibooks


text:
Bartending/Cocktails/Margarita

The margarita is the most common of all tequila-based cocktails. There are three main ingredients in a margarita: Tequila, Triple Sec, and lime juice. The traditional recipe is 3:2:1 – three parts Tequila, two parts Triple Sec and one part lime juice; however, the IBA standard is 7:4:3 = (50% tequila, 29% Triple Sec, 21% fresh lime or lemon juice), which keeps 50% tequila, but uses slightly less Triple Sec and correspondingly slightly more lime juice.

Other orange flavored liqueurs are frequently substituted for Triple Sec; Cointreau is most common, but there are many alternatives.

The rim of the glass is often, but not always, salted.

Traditional tequilas are dry, and served without ice; however, one may prepare sweet tequilas, often with other fruit juices such as pineapple, or serve over ice, or even blended. These sweet and iced variants are looked down upon by traditionalists, and despised as “party drinks”, but frequently served at parties.

Brief Recipe

 * salt rim of cocktail glass
 * mix tequila, triple sec, and lime juice (3:2:1)
 * shake, strain

Ingredients

 * Tequila – or mezcal, or sotol
 * Blanco (unaged) is most common and recommended, but reposado (aged under 1 year) is also often used, and añejo (aged 1 to 3 years) is sometimes used. The issue is that tequila is the focus of the drink, and conversely the margarita is the most common tequila cocktail. Blanco is most assertive, and the purest expression of agave, while reposado is gentler and with somewhat less agave and a little wood (from oak); añejo has less agave taste and makes a very gentle margarita.
 * 100% agave is recommended, as it is the focus; mixto (less than 100% agave) is significantly cheaper, but of inferior quality. If cost is an issue or if very sugary, mixto may prove acceptable, though one should compare with 100% agave before serving.
 * Widely varying grades of tequila are used in margaritas, from the cheapest grade to the fanciest. This significantly affects the quality and the cost, and comparison is strongly recommended.
 * Orange liqueur
 * Triple sec is most common, and cheap; brands vary in quality and price. Cointreau is a common substitute, and significantly more expensive, but considered by many to be far superior to triple sec. Grand Marnier is another well-respected orange liqueur, of similar quality and price to Cointreau, while Patrón Citrónge is a more recent addition, somewhat cheaper than both, and Gran Gala is an Italian version that is again somewhat cheaper. There are many alternatives for orange liqueur, some little-known and little-advertised; curaçaos may also be used.
 * Issues to consider in orange liqueur include: alcohol content – orange liqueurs vary in alcohol content from 15% to 40% (30 to 80 proof); neutral spirits base (such as Cointreau) or brandy base (such as Grand Marnier) – this affects taste and color; and price – generic triple sec adds negligibly to the price of a margarita (compared to tequila), while name brands can double the price.
 * Citrus juice – or other fruit juice
 * Most often fresh lime juice, ideally from key limes; Persian limes are most common in stores, however. One can also use other citrus such as lemon, or even others such as grapefruit, though this is properly a variant. One may even use other fruit juices (as is common in daquiris), though this should be flagged.
 * Fresh lime juice is strongly recommended, and considered a defining characteristic; one may use Rose’s lime juice or sour mix, but this yields a significantly sweeter drink due to added sugar, and is considered deeply inferior.
 * Salt
 * Generally coarse salt is used; one may also use fine salt, or various flavored salts or sugar (of various fineness) instead.
 * Simple syrup
 * Some serve sweet tequilas; this is most easily accomplished by using simple syrup, sour mix or pre-packaged “tequila mixes”. Sweet margaritas are looked down upon as “party drinks”, and subtle details of the tequila or orange liqueur tend to be masked by the overwhelming sugar flavor, but they are widely served at parties.
 * Glass
 * Most formally a cocktail glass is used, as the classic margarita is a classic drink. Alternatively one may use an old-fashioned glass, particularly if serving on the rocks, or serve in a specialized margarita glass, particularly when serving with a blended fruit margarita.

Ratios
Ratios vary; they almost universally adhere to the order of tequila, triple sec, lime: the focus is tequila, and extra lime would yield a very sour drink.
 * 2:1:1 = 6:3:3 (50% tequila, 25% Triple Sec, 25% lime).
 * 3:2:1 = 6:4:2 (50% tequila, 33% Triple Sec, 17% lime).
 * 3:1:1 = 6:2:2 (60% tequila, 20% Triple Sec, 20% lime).
 * 1:1:1 = 6:6:6 (33% tequila, 33% Triple Sec, 33% lime) – a very sour variant.
 * IBA standard: 7:4:3 = (50% tequila, 29% Triple Sec, 21% lime),
 * in the amounts of 35 ml (seven parts) tequila; 20 ml (four parts) Cointreau or Triple Sec; and 15 ml (three parts) lemon or lime juice.

For overall amounts, one often uses 1.5 oz. or 2 oz. of tequila; the juice of half a lime is then enough. A cocktail glass, in which a margarita is generally served, can hold 2 such margaritas (assuming no ice), as reflected in the IBA standard quantities, and margaritas are mostly alcohol, so a full cocktail glass of margarita is a significant amount of alcohol.

Procedure

 * 1) (Optional) Salt the rim – rub the rim of a cocktail glass with a lime wedge (or half) or paper towel, dip in coarse salt.
 * One often takes care to coat only the outside of the rim by only rubbing the outside with the lime or towel, and rotating the outside of the rim through a salt dish (rather than dipping the entire rim into a dish of salt), and then shaking (after a brief pause for drying), so that the salt does not fall into the drink.
 * One may also salt half the rim, or salt most of the rim but leave a gap, allowing the drinker the option of a salted or unsalted rim.
 * More simply, one may ask the drinker their preference.
 * Salt may be omitted as interfering with the flavor of the tequila, or used to mask the flavor of an inferior tequila.
 * Alternatively, for sweet tequilas one may use sugar instead on the rim.
 * One may pre-salt glasses, as this is time-consuming and there is little loss from doing so ahead of time.
 * 1) Mix tequila, orange liqueur, and citrus juice.
 * 2) Shake (over ice)
 * One may alternatively stir, but shaking is preferred for mixing with fruit juices, and the tequila is a strong drink, so the ice shards of shaking are of little consequence or even a benefit.
 * 1) Strain
 * Some serve tequila on the rocks, though more purely it is served strained.
 * 1) (Optional) Garnish with a lime wedge or slice.

Sample amounts
3:2:1:
 * 1.5 ozs. tequila
 * 1 oz. orange liqueur
 * .5 oz. lime juice

2:1:1:
 * 2 ozs. tequila
 * 1 oz. orange liqueur
 * 1 oz. lime juice

(Optional): salt for rim

Pre-Mixed Margarita
Serve in a sugar or salt rimmed glass, on the rocks or with crushed ice.
 * 2/3 cup margarita mix
 * 1/3 cup generic tequila.

Ice-blended Margarita

 * 1 ½ oz. Tequila
 * ½ oz. orange liqueur
 * ½ oz. lime juice plus 1 lime wedges
 * 1 ½ cups ice cubes

Procedure

 * 1) In a blender, combine the ingredients and blend until slushy.
 * 2) Pour into prepared margarita glass and serve with a lime wedge.

Fruit Juice
Fruit juices can also be added to a Margarita. Examples of such combinations that go well are:
 * Lime juice with raspberry.
 * Strawberry or peach, with lemon juice.

Note, however, that fruit Margaritas are not recognised as part of the standard Margarita repertoire.

Ingredients:

 * 2 1/2 oz Prickly Pear Infused Tequila (Voodoo Tiki Desert Rose)
 * 1/2 oz triple sec
 * 2 oz sour mix
 * 1/2 oz orange juice
 * dash of grenadine to color
 * sugar coated lime wheel for garnish
 * salt or sugar for rimming

Preparation:

 * 1) Pour the ingredients into a cocktail shaker with ice.
 * 2) Shake well.
 * 3) Strain into a chilled margarita glass with a sugar or salt rim.
 * 4) Garnish with a sugar coated lime wheel.

Similar drinks

 * Daiquiri – a basic rum sour; rum-based blended ice and fruit drinks are known as fruit daiquiris, analogously to fruit margaritas

title: Bartending/Cocktails/Margarita


text:
User:JoshMcCracken

See me at Wikipedia.

title: User:JoshMcCracken


text:
Talk:Proteomics/Protein - Protein Interactions

Contributions commented out
I (Amanda) commented out a few chunks of text that were added by an unnamed user. This textbook is part of a class project, and this chapter is a collaboration between two students. Obviously, here on Wikibooks, everything is open to public editing and additions. I just want to prevent any confusion for myself, Lorelle, our profressor, and the classmates that will be reviewing our page. We will read all additions made and consider incorporating them into our writing. No information will be permanently deleted. However, until after this project is graded, we will continue to edit the page to display only work by ourselves and our classmates. Thanks for your understanding, and your interest in our Wikibook!

Amsitterly 20:36, 19 April 2006 (UTC)


text:
Adventist Youth Honors Answer Book/Arts and Crafts/Paper Maché

1. Name at least three kinds of bases upon which paper models may be shaped.
When wet, paper maché has very little form and will not hold its shape. So the first step in making a paper maché project is to make a base onto which the paper maché is applied. Bases can be made from many different items, including:
 * 1) Balloons: Inflate a balloon and tape other items onto it, such as paper cups, toilet paper rolls, or other items.
 * 2) Plastic bottles: Attach golf tees for legs to turn a plastic bottle into an animal (such as a pig).
 * 3) Aluminum Foil: Press the foil around a person's face to get an image of it. If the subject wears glasses, leave them on.  Carefully remove the foil and place crumpled newspaper into it to help hold the shape.
 * 4) Paper Plates: These make an excellent base for constructing a mask.
 * 5) Cardboard Boxes: Use small cardboard boxes such as those in which many food items are packaged.
 * 6) Wire and Wire Mesh: Form wire into the desired shape. Especially useful for this is fencing wire (such as chicken wire) and gutter guard mesh.  Hardware cloth is a little too stiff to work with.

a. Know how to prepare successful pulp
Pulp is paper which has been shredded into tiny pieces. First tear the paper (newsprint works well) into small pieces. In some instances, this will be good enough, but if you need finer pulp, throw the paper into a blender with some water. You can also get good raw material from an office paper shredder. When the pulp is as fine as you desire, add white glue and wallpaper paste. Amounts are not given here - you need to experiment to find a consistency that works well for what you are tring to do. Once it's mixed with glue, the pulp can be shaped like clay, or you can layer it onto a base.

b. Know how to prepare the glue
Mix the flour into the water thoroughly with your hands, being sure to break up all the lumps. You might try heating the mixture too, but do not let it come to a boil. You can vary the amount of flour or water to make the glue thicker or thinner. Experiment to find what works best for you.
 * 6 cups water
 * 1 cup flour

You can also add a few tablespoons of bleach to retard the growth of mold, but make sure everyone who is going to use the paste knows that you did this - after all, flour and water are the same ingredients that you use to make bread, and you don't want your Pathfinders performing any taste-tests on a bleach-laden batch of glue!

Glue is used with strips of paper which are layered onto the base. When the glue dries, the paper stays in place and binds together forming a (hopefully) beautiful sculpture.

3. Be familiar with all ingredients and know why they are used.

 * Here are some thoughts on the paste from Wikipedia: Paper Maché

 * Paper-mâché paste is the substance that holds the paper together. The traditional method of making paper-mâché paste is to add one part water to one part flour. Some artists prefer to boil the paste, saying that it makes the consistency smoother. Water to flour ratio is changed to five parts water to one part flour in this case. Other artists use a three to one or a one to one ratio of water and Polyvinyl acetate (PVA glue). Still others say that starch makes a fine paste. Adding a dash of cinnamon to the mixture gives the paste a pleasant smell; adding a dash of salt reduces the chances of the product developing mold.

6. Submit articles to examiner and have workmanship approved.
As the instructor, you will be responsible for judging the workmanship of the projects. The most important consideration is that you apply a fair standard and not show favoritism. Pathfinders are quickly able to detect unfairness, as it is an extremely important concept to them.


text:
MATLAB Programming/Axis Handle

MATLAB offers incomparable control over the way you can add details to your plot. From inserting text at the right positions to labelling the axes, MATLAB from the command line offers you an easy way to create publication style graphics. With support for Encapsulated PostScript and Adobe Illustrator output. Complex figures with several axes and conveying large amounts of information can be created.

Concept of a handle
Most operations on figures generate objects with a set of properties. Users familiar with object-oriented programming would realize that the functions and the data are encapsulated into the object. A typical figure would contain at least half a dozen objects. These objects are called handles. A very tacky analogy would be like handles to several different refrigerators with several different contents. To provide an intuitive feel. I have listed out the properties from a text handle.

Finding a handle
Various commands provide required handles, for example: h = gcf; % Get current figure h = gca; % Get current axis

Axis Label
xlabel labels the x-axis of the current plot. You can display text on two lines or insert the value of variables ylabel labels the y-axis of the current plot. It works in same way of xlabel, but the output is vertical in 2D plots.

title: MATLAB Programming/Axis Handle


text:
D Programming/GNU D Compiler

GDC is a open-source D compiler using GCC as back end and parts of DMD in the front end. The current version is 0.24 which is based on DMD 1.020.

The website can be found at http://dgcc.sourceforge.net/

An updated effort to help get GDC updated can be found at http://bitbucket.org/goshawk/gdc/wiki/Home

Install GDC on Debian or Ubuntu
GDC is available in Ubuntu Repositories since 7.10 (Gutsy Gibbon).

Also, a debian package does exist for version 0.22 of the GNU D Compiler front end. See http://gdcgnu.sourceforge.net/

Joakim Karlsson has previously made shell script for automatic install. It needs to be updated for the latest version of the GNU D Compiler and the GCC Version.

PREFIX=/opt/gdc GCC_PACKAGE=gcc-4.0 GDC_SOURCE=gdc-0.17.tar.bz2 GDC_URL=http://home.earthlink.net/~dvdfrdmn/d/${GDC_SOURCE} mkdir gdc cd gdc apt-get source ${GCC_PACKAGE} tar xzf gcc*.orig.tar.gz cd *.orig tar xjf *.tar.bz2 cd gcc* cd gcc wget ${GDC_URL} tar xjf gdc*.tar.bz2 cd .. gcc/d/setup-gcc.sh cd .. gcc*/configure—prefix=${PREFIX} --enable-languages=d make sudo make install
 * 1) !/bin/sh

title: D Programming/GNU D Compiler


text:
Python Programming/Extending with C++

There are different ways to extend Python with C and C++ code:
 * In plain C, using Python.h
 * Using Swig
 * Using Boost.Python, optionally with Py++ preprocessing
 * Using pybind11
 * Using ../Cython/.

This page describes Boost.Python. Before the emergence of Cython, it was the most comfortable way of writing C++ extension modules.

Boost.Python comes bundled with the Boost C++ Libraries. To install it on an Ubuntu system, you might need to run the following commands $ sudo apt-get install libboost-python-dev $ sudo apt-get install python-dev

setup.py
Now we can build our module with

python setup.py build

The module `hello.so` will end up in e.g `build/lib.linux-i686-2.4`.

Using the extension module
Change to the subdirectory where the file `hello.so` resides. In an interactive python session you can use the module as follows. >>> import hello >>> hello.say_hello("World") Hello World!

An example with CGAL
Some, but not all, functions of the CGAL library already have Python bindings. Here an example is provided for a case without such a binding and how it might be implemented. The example is taken from the CGAL Documentation.

We then compile and run the module as follows: $ python setup.py build $ cd build/lib* $ python >>> import test >>> test.create_tree Window Query: 3,2.1:c 8,5.1:a Done >>>

Handling Python objects and errors
One can also handle more complex data, e.g. Python objects like lists. The attributes are accessed with the extract function executed on the objects "attr" function output. We can also throw errors by telling the library that an error has occurred and returning. In the following case, we have written a C++ function called "afunction" which we want to call. The function takes an integer N and a vector of length N as input, we have to convert the python list to a vector of strings before calling the function.

title: Python Programming/Extending with C++


text:
Category:Winter ingredients

Ingredients that are in season in winter. For more detailed information on seasonality, consult the seasonality page or the relevant paragraph on the ingredient page.

title: Category:Winter ingredients


text: Template:New honor warning

title: Template:New honor warning


text:
User:Super Dave~enwikibooks

Hello my name is David N B. I created a Wikibook account because I wanted to help improve on the Wikibook Blender 3D: Noob to Pro.

While also learning to become a Pro instead of a Noob at Blender 3D

title: User:Super Dave~enwikibooks


text:
Category:Spring ingredients

Ingredients that are in season in spring. For more detailed information on seasonality, consult the seasonality page or the relevant paragraph on the ingredient page.

title: Category:Spring ingredients


text:
User talk:216.195.247.107

Just a friendly note to say I think what you're adding is already in Bartending/Cocktails/Glossary, Jguk 06:15, 20 April 2006 (UTC)

title: User talk:216.195.247.107


text:
User talk:209.51.66.192

Please stop adding a WoW tag. The discussion on WB:VIP suggests that not only do most users see no advantage in it, but a disadvantage. As the accounts you highlight are all banned indefinitely and so can't be used again, there is no benefit in highlighting them, Jguk 06:23, 20 April 2006 (UTC)

The tag is added on Wikipedia to alert other Wikimedia projects of accounts with a WoW affiliation, wether by nomenclature or by actual page move vandalism, and I thought the reason for the WoW tag at Wikibooks was for the same reason. I won't add it anymore then, sorry :( 209.51.66.192 18:53, 20 April 2006 (UTC)

 * No problem at all. It's just that WB is a different project with different rules. Hopefully you'll be able to contribute more to Wikibooks in te future, Jguk 21:10, 20 April 2006 (UTC)

title: User talk:209.51.66.192


text:
Umbraco/Installation/Installing Umbraco on Windows XP Professional

THIS DOES NOT WORK WITH UMBRACO VERSION 3 OR 4
By Claus Nedergaard – Nedergaard Design & Marketing, Denmark.

A guide to the First time Installation of

 * IIS 5.1
 * .Net Framework
 * MSDE 2000
 * Database Manager
 * Umbraco CMS 2.1.1
 * additional copies of Umbraco CMS 2.1.1

on Windows XP Professional

Install IIS 5.1 on Win XP Pro

 * Choose Control Panel -> Add Programs.
 * Choose Add/Remove Windows components – then pick IIS and press next. ( You need the XP Pro cd for this). And then Finish.
 * Now you have the Inetpub folder on your root directory – C:\inetpub. It contains the web, mail, ftp folders

Install .NET Framework on Win XP Pro
- or -
 * Autorun the Win XP Pro cd. From the menu choose install .Net Framework. Follow the onscreen instructions
 * Download the .NET Framework 1.1 from Microsoft and install it

 * Restart the computer

Install MSDE on Win XP Pro

 * Download and run MSDE200A installer from Microsoft
 * Follow the on screen advice/commands. (unpacks files in c:\msde2000a
 * Open DOS command prompt.
 * Type -> cd c:\msdeRelA
 * Type-> setup SAPWD=”YOURCHOISEOFPASSWORD” securitymode=SQL  –> press enter  ( The default installation of msde uses windows authentication by default).
 * Restart the computer

Install MSDE Manager on Win XP Pro

 * Download and run Setup_DbaMgr2k
 * Follow the onscreen instructions.

Install Umbraco 2.1.1

 * Create folder for website in c:\inetpub\wwwroot\’website name’
 * Copy all files from the Umbraco21.zip folder to that folder.
 * Change permissions for the ‘data, media, css, xslt,user controls’ folders. But first change the default file permissions for win xp. See below.

Change default file permissions for Win XP

 * Pick Start -> This Computer.
 * In the top menu choose Functions -> Folder options.
 * Choose Show (Vis).
 * Uncheck the ‘Simple file sharing’ box.
 * Now you can change the permissions. Pick all 5 folders (css, media, data, xslt, user controls) – right click and choose Properties.
 * Pick Security tab. Pick Add..
 * Type aspnet in the text box and click Ok.
 * Check Modify (Redigering) to allow modify and write permission to aspnet account.

Create Website

 * Open IIS and right click Default Site (Standardwebsted) -> New -> Virtual Folder.
 * Follow the onscreen guide -  Type website name and copy it.
 * Choose folder (c:\inetpub\wwwroot\’website name’)
 * Give read access and permission to run scripts (ASP). Finish the guide
 * Cut the umbraco_client folder out of your webfolder and place it in the Default Site folder so it is at the same node (gren) as the website itself. (This seems silly but nevertheless necessary to make umbraco run in XP Pro).
 * Right click the webfolder if necessary and make the root folder your websitefolder.

Create new database

 * Create new database – Open Database Manager
 * Choose databases -> right click and pick ‘New Database’
 * Enter database name and choose path for the database (c:\inetpub\wwwroot\’website name’\data\database_name)
 * Save and close window
 * Open Logins and type a Name and a Password in the ‘General tab’. In the ‘Default connection information’ you pick the database to attach the Login to.
 * Pick the ‘Database access’ tab. Choose your database by marking it. In the ‘Database roles’ you pick db_owner, db_datareader, db_datawriter. Save and close window
 * Open database and right click on Users – pick New User. Type the login and Name that was created under Logins. Check db_owner, db_reader, db_writer.

Edit Web.Config file

 * Open with Wordpad. Go to the bottom where it says …
 * Change the path name in these lines. Usually you have to add in the website name.

Default:

Edited:

 * Save and close the file.

Install Umbraco 2.1.1

 * Open Umbraco Interface in IE by typing your localhost and path – "http://localhost/UmbracoDemo1/install/default.aspx"
 * In the Umbraco 2.1 Configuration Wizard first window press Next.
 * Click Install and then Next.
 * You should now be looking at a page saying…’Your permission settings are perfect!’ – Click Next.
 * You might be asked to change your password. Change it!
 * Open the Web.Config file. Go to the bottom and find this line…

Now you add 211 to that line…

<add key="umbracoConfigurationDone" value="211"/>

 * Save and close file.
 * Click Next. Download the WebSiteWizard package.
 * Delete the install folder ’c:\inetpub\wwwroot\’website_name’\install’
 * Login to Umbraco ‘http://localhost/website_name/umbraco’ and enter Username and Password. Username is always ‘umbraco’ as default. Password is what you chose in the configuration when you were asked to change it.
 * Install sample website - Go to ‘Developer’ section. Right click on ‘Macros’ -> choose ‘Import Package’
 * Follow onscreen instructions to configure sample website

Getting the websiteWizard .umb package to work on your new Umbraco site
If you have followed these instructions and put your copy of Unbraco in a subdirectory under your root directory (wwwroot\yoursite) then you will need to make some changes to the CSS and Template files of the websiteWizard.umb package after you install it if you want to see the site properly. After installing the websiteWizard package:

<link rel="stylesheet" href="/yoursite/css/wizard.css" type="text/css"> <a href="/yoursite/" title="Back to front page" id="header" style="background: url(/yoursite<?UMBRACO_GETITEM field="headerImage" recursive="true"/> "> background: url(/yoursite/css/wizard/pullBackground.png); At this point your Wizard based site should render as expected. Many thanks to Thomas Höhler for this tip. - Cecil Thornhill, USA
 * open the template folder and edit the Main template. Add your path information to the CSS includes so that they are used to render the page.
 * add your path information to the URLs for the header image and top background image.
 * open the Wizard CSS file and add your path information to the pullBackground.png reference so the graphic can be found.

Place Umbraco files on the computer

 * Create folder for website in c:\inetpub\wwwroot\’website name’
 * Copy all files from the Umbraco21.zip folder to that folder.
 * Change permissions for the ‘data, media, css, xslt,user controls’ folders.
 * Pick all 5 folders (css, media, data, xslt, user controls) – right click and choose Properties.
 * Pick Security tab. Pick Add..
 * Type aspnet in the text box and click Ok.
 * Check Modify (Redigering) to allow modify and write permission to aspnet account.

Create Website

 * Open IIS and right click Default Site (Standardwebsted) -> New -> Virtual Folder.
 * Follow the onscreen guide -  Type website name and copy it.
 * Choose folder (c:\inetpub\wwwroot\’website name’)
 * Give read access and permission to run scripts (ASP). Finish the guide
 * Right click the webfolder if necessary and make the root folder your websitefolder.
 * Under the Documents tab add default.aspx and move it to the top of the list

Create new database

 * Create new database – Open Database Manager
 * Choose databases -> right click and pick ‘New Database’
 * Enter database name and choose path for the database (c:\inetpub\wwwroot\’website name’\data\database_name)
 * Save and close window
 * Open Logins – right click and choose new login. Type a Name and a Password in the ‘General tab’. In the ‘Default connection information’ you pick the database to attach the Login to.
 * Pick the ‘Database access’ tab. Choose your database by marking it. In the ‘Access granted to database for this login’. In ‘Database roles’ you pick db_owner, db_datareader, db_datawriter. Save and close window
 * Open database and right click on Users – Check to see if your newly created Login is visible under ‘Users’. If not pick New User. Type the login and Name that was created under Logins. Check db_owner, db_reader, db_writer.

Edit Web.Config file

 * Open with Wordpad. Go to the bottom where it says …<appSettings>
 * Change the path name in these lines. Usually you have to add in the website name.

Default: <add key="umbracoReservedUrls" value=",/umbracoTextGen.aspx,"/> <add key="umbracoReservedPaths" value="/umbraco/,/install"/> <add key="umbracoContentXML" value="/data/umbraco.xml"/> <add key="umbracoStorageDirectory" value="/data"/> <add key="umbracoPath" value="/umbraco" /> <add key="umbracoDbDSN" value="Server=127.0.0.1;Database=YOUR_DATABASE;	User ID=YOUR_USER;Password=YOUR_PASSWORD;	Trusted_Connection=False"/> <add key="umbracoSmtpServer" value="127.0.0.1"/>

Edited: <add key="umbracoReservedUrls" value=",/Websitefolder_name/umbracoTextGen.aspx,"/> <add key="umbracoReservedPaths" value="/ Websitefolder_name/umbraco/,/ Websitefolder_name /install"/> <add key="umbracoContentXML" value="/Websitefolder_name/data/umbraco.xml"/> <add key="umbracoStorageDirectory" value="/Websitefolder_name/data"/> <add key="umbracoPath" value="/Websitefolder_name/umbraco" /> <add key="umbracoDbDSN" value="Server=YourServerName;Database=YOUR_DATABASE;	User ID=YOUR_USER;Password=YOUR_PASSWORD;	Trusted_Connection=False"/> <add key="umbracoSmtpServer" value="127.0.0.1"/>

 * Save and close the file.

Install Umbraco 2.1.1

 * Open Umbraco Interface in IE by typing your localhost and path – ‘http://localhost/website_name/install/default.aspx'
 * In the Umbraco 2.1 Configuration Wizard first window press Next.
 * Click Install and then Next.
 * You should now be looking at a page saying…’Your permission settings are perfect!’ – Click Next.
 * You might be asked to change you password. Change it!
 * Open the Web.Config file. Go to the bottom and find this line…

<add key="umbracoConfigurationDone" value=""/>

Now you add 211 to that line…

<add key="umbracoConfigurationDone" value="211"/>

 * Save and close file.
 * Click Next. Download the WebSiteWizard package.
 * Delete the install folder ’c:\inetpub\wwwroot\’website_name’\install’
 * Login to Umbraco ‘http://localhost/website_name/umbraco’ and enter Username and Password. Username is always ‘umbraco’ as default. Password is what you chose in the configuration when you were asked to change it.
 * Install sample website - Go to ‘Developer’ section. Right click on ‘Macros’ -> choose ‘Import Package’
 * Follow onscreen instructions to configure sample website


text:
User talk:Greyfox~enwikibooks

Greyfox 12:59, 20 April 2006 (UTC)

earthbound is an rpg for the snes and has a wonderful storyline

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Greyfox. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Greyfox~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:15, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:00, 19 April 2015 (UTC)

title: User talk:Greyfox~enwikibooks


text:
Guide to First Year Teaching/What to Expect

As a teacher nearing the end of my first year, I have learned so much! A few things you can definitely expect:

Everything you think you know will probably change From what you expect from your students to your homework policy down to your lesson plans, you will discover things that work wonderfully and some things not at all. My classroom has not been the most organized or most efficiently run this year. So, I have already begun new plans for next year. The biggest thing I am changing is my homework policy. I did a really terrible job of getting my students to turn their work in on time, mostly because there was no accountability, but next year things are going to be different. I am also changing the structure of my classroom. Well, maybe I should say I am putting a firmer structure into place. I have learned structure is everything!

Students will test you As a new teacher, the students will try to get everything by you. They want to see what they will be able to get away with. You must begin being firm from the very start and let them know that you are in charge.

Lesson plans always change It is difficult planning lessons too far in advance because inevitably something will happen that will put you behind. Just learn to go with the flow, be flexible, and don't let it stress you out.

Spring is extremely busy When other teachers tell you this, BELIEVE them. I knew that the spring would be busy, but I had no idea it would be crazy. Make sure during the fall semester that you are using your time wisely and covering as much information as possible, especially if you teach a TAKS subject. When spring rolls around, you can expect lots of absent students for extracurricular activities and lots of catch-up work. Just be prepared.

These are only a few things you should probably know before going into your first year; there are countless others. Hopefully this will help!


text:
Talk:Primary Mathematics/Numbers

Hi,

I am new with this but see that it really has a great potential for teaching and learning and would like to join. Being a Math teacher I am involved with a program that also teaches Basic Math to people who have no idea about Math. I saw the numbers Unit and realized that there could be useful addition to that because the basic numbers 0,1,2...9 are just the basic symbols. The next step is to explain the placement value notation and one can use this opportunity to tie it with different number bases (binary for example).

How do I go by adding a module? Is it reviewed by others before it is being added?

I will appreciate if I could Email to ask specific questions for example:

what does this mean: Place comments that start a new topic at the bottom of the page and give them == A Descriptive Header ==.

Dubimax 15:12, 20 April 2006 (UTC)Dani

 * I'm an ex-maths teacher with experience of 7yr olds to adults. I've been looking for a suitable place to add content. If you are still there, Dubimax, I've taken the liberty of adding to your page. As far as finding our way around, I'll be learning with you. Barry Desborough 18:03, 28 October 2006 (UTC)

title: Talk:Primary Mathematics/Numbers


text:
Green Politics

Historically, environmental issues in conflict with human growth and development, Green Politics pre-date the Agrarian Revolution. The individual's and group's survival often determined the direction of decision making based upon material needs. Thus, the individual and the group's needs were bound in the environmental security of all as well as the creation of a sustainable population. Political structures reflected the group's material needs.

Currently expressed in popular terms by corporate media and others as a "political party," Green Politics has a much broader, deeper meaning. One significant example of the growth of Green Politics in the 20th Century occurred as environment, women, nuclear, and other like-minded groups joined together under the banner of Green Politics:

Green Politics - the four pillars of Green politics: ecology, nonviolence, social justice, and grassroots democracy.

Green politics grew from a linking of social and environmental movements in response to the nation-states' cold war MAD (mutually assured destruction) nuclear policies, general environmental degradation worldwide, war, patriarchal top-down power structures, and civil liberties' issues. "Green" represents the color of the greatest mass of life on earth, and an easy umbrella with applicable connotations to help unify these diverse movements. Ecology's life focus and implications quickly became a central organizing principle.

Additionally, from a Green perspective, the cold war nations' economic systems of socialism, communism, and capitalism represent growth economies incompatible with human and non-human nature. For example, the Communist Party of the USA (CPUSA) advocated nuclear fusion research and development as do many Democrats and Republicans. Generalizing from an ecologically informed perspective, such developments are irresponsible and environmentally unethical. One soon sees how Green politics develops from the idea that ecology is the "subversive" science because its implications undermine the intellectual, ethical, and moral standing of previous political and economic ideologies.

One "lives" Green politics to some degree. For Greens, applying the lessons of ecology to individual and social responsibility issues within the context of holistic thinking and action creates an obvious need for participatory democracy. "Politics" in this sense becomes a daily activity, series of choices, and continuing social and life sciences education. Moreover, individual and social responsibility within an ecological context require this bottom-up approach to decision making. Noteworthy, although the most publicized, electoral politics under the Green umbrella represents but "one leg"of Green politics. (See Green Parties of the ASGP for an application of Green Politics in electoral politics.)

Goals: Greens think that the dominant political and economic system will collapse (as it is ecologically) while ecological and political crises grow. Greens hope to create a Green society "parallel" to the dominant society and thereby mitigate the damages of collapsing ecological, economic, and political systems. (See The Ten Key Green Values and "A Green Political Philosophy" for more) The idea is to peacefully overgrow governments, the corporate state, and ruling ideologies in a peaceful, ecological manner. Greens are inherently pacifist.

" In Green politics, we practice tenderness in relations with others; in caring for ideas, art, language, and culture; and in cherishing and protecting the Earth. To think Green is to build solidarity with those working for social justice and human rights everywhere, not bound by ideologies. -Petra Kelly"(return to What Greens Think)

 * /Technology/

title: Green Politics


text:
Green Politics/Technology

Green Politics and Technology

Green Politics posits the need for appropriate technology in the context of ecological relationships for the human species as well as all other native species-populations.

Technology - Many Greens perceive technology as a way to liberate humanity from the drudgery and boring grind of physical labor. In this sense, technologies have a liberating destiny for humanity. Greens still question technology ruthlessly, because technology is either appropriate or inappropriate.

Also, science, technology, and production are now fused in an attempt to continually increase production and consumption. As a result, inappropriate technologies flourish as this insatiable appetite for growth expands. Inappropriate technologies spread like plagues World-wide while commercial propaganda replaces vital information to extend inappropriate technologies.

Here's one way to understand inappropriate technologies: Firing a cannon ball to ring a doorbell is an inappropriate use of technology, not so unlike using nuclear energy to produce electricity. The cannon in this example also represents an inappropriate technology, many Greens will argue. "Its destiny is implied by its design."

Be that as it may, the cannon's influence ends at the doorbell. However, the technologies of genetic engineering, for another example, alter life forms. Like the cannon, genetic engineering has a destiny in its design; unlike the cannon, genetic engineering's destiny influences human and non-human nature well beyond the perceivable future. Ecological problems will probably grow exponentially because one in five non-indigenous (not native born) species, when introduced into a new habitat, dislodge indigenous (native born) species-populations.

Consequently, future generations may choose to ignore the cannon's destiny and deny it a place in their society. But, they cannot choose to ignore genetic engineering's destiny or deny it a place in their society, since our generation embedded altered life-forms in non-human nature. Ecological collapse will most likely occur if humanity fails to change its attitude toward nature. The same reasoning applies to other inappropriate technologies that risk life's ecological security, like nuclear energy.

title: Green Politics/Technology


text:
Georgia Water/Laws/Codes

Federal Laws

 * 7 USC 2321 - U.S. Plant Protection Act
 * 16 USC 1271 - U.S. Wild and Scenic Rivers Act
 * 16 USC 1361 - U.S. Marine Mammal Protection Act
 * 16 USC 1451 - U.S. Coastal Zone Management Act
 * 16 USC 1531 - U.S. Endangered Species Act
 * 16 USC 3501 - U.S. Endangered Species Act
 * 16 USC 460 - U.S. Land and Water Conservation Fund Act
 * 16 USC 4701 - U.S. National Invasive Species Act
 * 16 USC 669 - U.S. Federal Aid in Wildlife Restoration Act
 * 16 USC 703 - U.S. Migratory Bird Treaty Act
 * 16 USC 777 - U.S. Federal Aid in Sport Fish Restoration Act
 * 33 USC 1251 - U.S. Clean Water Act
 * 42 USC 300 - US Safe Water Drinking Act
 * 42 USC 4321 - U.S. National Environmental Policy Act
 * U.S. Convention on International Trade in Endangered Species
 * U.S. Executive Order 13112

State Laws

 * O.C.G.A. § 12-2-8 - Planning Act of 1989
 * O.C.G.A. § 12-2-8 - Mountain and River Corridor Protection Act
 * O.C.G.A. § 12-3-600 - Nongame Wildlife Conservation Programs Act of 1985
 * O.C.G.A. § 12-3-70 - Heritage Trust Act of 1975
 * O.C.G.A. § 12-3-90 - Natural Areas Act
 * O.C.G.A. § 12-4-70 - Surface Mining Act
 * O.C.G.A. § 12-5-120 - Waterwell Standards Act
 * O.C.G.A. § 12-5-170 - Safe Water Drinking Act
 * O.C.G.A. § 12-5-20 - Water Quality Control Act
 * O.C.G.A. § 12-5-230 - Shore Protection Act
 * O.C.G.A. § 12-5-280 - Coastal Marshlands Protection Act of 1970
 * O.C.G.A. § 12-5-31 - Surface Water Use Act
 * O.C.G.A. § 12-5-320 - Coastal Management Act
 * O.C.G.A. § 12-5-350 - Scenic Rivers Act of 1969
 * O.C.G.A. § 12-5-370 - Safe Dams Act of 1978
 * O.C.G.A. § 12-5-470 - Water Supply Act
 * O.C.G.A. § 12-5-520 - Comprehensive Statewide Water Management Planning Act
 * O.C.G.A. § 12-5-540 - Flint River Drought Protection Act
 * O.C.G.A. § 12-5-90 - Groundwater Use Act
 * O.C.G.A. § 12-6-170 - Wildflower Preservation Act of 1973
 * O.C.G.A. § 12-7-1 - Erosion and Sedimentation Act of 1975
 * O.C.G.A. § 12-16-1 - Environmental Policy Act
 * O.C.G.A. § 27-1-1 - Game and Fish Code
 * O.C.G.A. § 27-3-130 - Endangered Wildlife Act of 1973
 * O.C.G.A. § 36-22-1 - Land Conservation Act
 * O.C.G.A. § 36-91-1 - Local Government Public Works Construction Law
 * O.C.G.A. § 44-10-1 - Uniform Conservation Easement Act
 * O.C.G.A. § 48-7-7.4 - Conservation Use Act of 1991 as amended
 * O.C.G.A. § 52-1-1 - Protection of Tidewaters Act
 * O.C.G.A. § 52-1-30 - Right of Passage Act
 * O.C.G.A. § 52-2-1 - Ports Authority Act
 * O.C.G.A. § 52-3-1 - Intracoastal Waterway
 * O.C.G.A. § 52-4-1 - Canal Companies
 * O.C.G.A. § 52-5-1 - Navigation Companies
 * O.C.G.A. § 52-6-1 - Pilots and Pilotage
 * O.C.G.A. § 52-7-1 - Boat Safety Act
 * O.C.G.A. § 52-8-1 - Dumping Navigation Impediments
 * O.C.G.A. § 52-9-1 - Beach Sand and Channel Dredging
 * Dumping Navigation Impediments
 * Endangered Wildlife Act of 1973
 * Environmental Policy Act
 * Erosion and Sedimentation Act of 1975
 * Flint River Drought Protection Act
 * Game and Fish Code
 * Groundwater Use Act
 * Heritage Trust Act of 1975
 * Intracoastal Waterway
 * Land Conservation Act
 * Local Government Public Works Construction Law
 * Mountain and River Corridor Protection Act
 * Natural Areas Act
 * Navigation Companies
 * Nongame Wildlife Conservation Programs Act of 1985
 * Pilots and Pilotage
 * Planning Act of 1989
 * Ports Authority Act
 * Protection of Tidewaters Act
 * Right of Passage Act
 * Safe Dams Act of 1978
 * Safe Water Drinking Act
 * Scenic Rivers Act of 1969
 * Shore Protection Act
 * Surface Mining Act
 * Surface Water Use Act
 * Uniform Conservation Easement Act
 * Water Quality Control Act
 * Water Supply Act
 * Waterwell Standards Act
 * Wildflower Preservation Act of 1973

title: Georgia Water/Laws/Codes


text:
Movie Making Manual/Cinematography/Cameras and Formats/RED

History of the camera
The Red One Digital Cinema Camera was unveiled at the NAB Exhibition 2006 in Las Vegas. An "Ultra-High-Definition" digital camera, it has a custom Bayer Pattern sensor array (the "Mysterium") with a resolution of 4900x2580 (4700x2540 active image area, 4520x2540 maximum recordable image area). It was designed as a replacement for traditional 35mm film cameras and has a number of recording resolutions including 2540p, 4k, 2k, 1080p, 1080i and 720p, though production models are limited to recording in 4k, 4k 16:9, QHD, 3k, and 2k, through sensor windowing. It is targeted specifically at the retail market and has a base price (without lenses or recorder) of $17,500. A number of RED accessories were simultaneously revealed, including two initial lenses, a 300mm prime and a 18-85mm zoom (though the camera will take standard PL and B4 mount lenses). Recording is done through a mirrored RAID-0 array of 160 GB hard drives, totalling 320 GB, through a 128 GB Solid-State Drive, or through a Compact Flash Module, which records to 8 or 16 GB cards produced to RED's specifications.

The RED One records in a compressed RAW Bayer format which the company claims to be visually lossless, though filmmakers have discovered certain reproducible artifacts of the encoding mechanism. While this allows the camera hardware to be produced at a reduced cost, comparable to other digital camcorders, which encode video onboard to an easily usable format, it also significantly complicates and extends post-production. Native support of Redcode in Non-linear Editors is not widespread, or mature, so RED's post-production workflow relies on company provided software for online editing, such as Redcine, and Red Alert, to encode to a digital intermediate format, such as ProRes, or DNxHD.

 * First 4k footage of the camera was shown at IBC 2006 in Amsterdam
 * A provisional date of early 2007 was announced for retail to the public.

David Stump ASC has tested a "Red" lab prototype for exposure and on a greenscreen but as of January 2007 development is not complete, and no stand-alone Red cameras exist yet. Many dp's that have invested in this technology have yet to figure out how they are going to edit with camera.

The above information is outdated; the Red camera has since been released and several movies were shot using Red camera.

Tech Specs

 * See official site

Tips and tricks

 * Lens buying tips (dvxuser.com)

Accessories

 * Recording Media (more info)
 * RED-DRIVE
 * REDFLASH
 * RED-RAID
 * RED-RAM

Films made with the camera

 * "Bookaboo" (2009)
 * "Flow" (2008)
 * "Leverage" (2008)
 * "Unnai Pol Oruvan"(2009) [Tamil Movie]
 * "LIVE - seedha sachh" (2010) (Hindi movie)
 * "The Social Network"(2010) Directed by David Fincher
 * "Saluda al diablo de mi parte" (2011) - Directed by Juan Felipe Orozco http://www.imdb.com/title/tt1262415/
 * "The Girl With the Dragon Tattoo" (2012) Directed by David Fincher

Links

 * Official Site
 * RedCamCentral.com unofficial forum
 * UK Red Digital Cinema Community

/Cameras


text:
Georgia Water/Laws/Names

Statutes listed by Alphabetically by Name

Federal Laws

 * Clean Water Act
 * Coastal Barrier Resources Act
 * Coastal Zone Management Act
 * Convention on International Trade in Endangered Species
 * Endangered Species Act
 * Executive Order 13112
 * Federal Aid in Wildlife Restoration Act
 * Federal Aid in Sport Fish Restoration Act
 * Land and Water Conservation Fund Act
 * Marine Mammal Protection Act
 * Migratory Bird Treaty Act
 * National Environmental Policy Act
 * National Invasive Species Act
 * Plant Protection Act
 * Safe Water Drinking Act
 * Federal Aid in Sport Fish Restoration Act
 * Wild and Scenic Rivers Act

State Laws

 * Beach Sand and Channel Dredging
 * Boat Safety Act
 * Canal Companies
 * Coastal Management Act
 * Coastal Marshlands Protection Act of 1970
 * Comprehensive Statewide Water Management Planning Act
 * Conservation Use Act of 1991

title: Georgia Water/Laws/Names


text:
Georgia Water/Laws/Planning Act of 1989

Georgia Planning Act of 1989, O.C.G.A. § 12-2-8

General Description
The Act gives the Georgia Department of Natural Resources the authority to establish minimum standards necessary to protect natural resources, including water resources. The minimum standards relating to water include the following topics: (1) watershed protection, including buffers and development density; (2) groundwater protection, including land use activities; (3) wetland protection, including land use and alteration of wetlands; (4) protection of river corridors; and (5) mountain protection, including regulation of wells and septic tanks. The Department can adopt different standards for different areas of the state depending on the specifics of that area.

Specific Protections
Perennial river corridors are to be protected by a minimum 100 foot buffer on both sides, measured from the stream bank. There is an exception for single-family homes, though any septic tank drainfield must be outside the buffer. There is also an exception for roads and utilities under some circumstances.

Local and Regional Planning
The statute requires local and regional governments to identify and map river corridors in conjunction with developing land use plans. The statute then lists considerations that local land use plans must address.

title: Georgia Water/Laws/Planning Act of 1989


text:
US History/Keywords2

Civil War and Reconstruction (1860-1877)
Jefferson Davis Abraham Lincoln First Battle of Manasses (Bull Run) Second Battle of Manasses (Bull Run)

New South, Old West, Gilded Age, Populism, Imperialism (1870-1900)
Jim Crow Ku Klux Clan Sinmiyangyo Charles H. Winfield

1900-WWI
aeroplane Silent Film RMS Titanic RMS Brittanic

World War I
War to End All Wars World War Kaiser Hoch, hoch der Kaiser! von Hindenburg ist mein Vater! Tsar Austria-Hungary Flying Circus Trotsky Мы - We (Novel) Mustafa Kemal Atatürk The Lost Battalion

title: US History/Keywords2


text:
US History/Keywords3

Roaring 20s (Lost Generation)
Gay 80s Gay 90s Women's Suffrage Prohibition Red Scare Second International income tax "New Negro" Jazz Esperanto League of Nations (United Nations) Cheaper by the Dozen The Sun Also Rises Al "Scarface" Capone "Bugs" Muran Valentine's Day Massacre Bonnie and Clyde anti-Modernism

Depression
Hoover Third Riff War Lina Medina Franklin Roosevelt (FDR)

Spanish Civil War (Guerra Civil Española)
Popular Front Francisco Franco Calros Garcias Pope Pius XII Ernest Hemingway For Whom the Bell Tolls Tierra Española

World War II
Free World Slave World mind control Josef Stalin Adolf Hitler Emperor Hirohito Swastika Nazi fascist yellow star total war (totalier Kreig) SNAFU Winston Churchill D-Day Pearl Harbor Allies

title: US History/Keywords3


text:
Formal Logic/Sentential Logic/Start of Sentential Logic

Start of Sentential Logic A Sub-Book of Formal Logic

Places to go
 * Forward to the first page of Sentential Logic.

 * Backward to the last page of Preliminaries.


text:
Formal Logic/Preliminaries/End of Preliminaries

End of Preliminaries A Sub-Book of Formal Logic

Places to go
 * Forward to the first page of Sentential Logic.

 * Backward to the last page of Preliminaries.


text:
Formal Logic/Preliminaries/Start of Preliminaries

Start of Preliminaries A Sub-Book of Formal Logic

Places to go
 * Forward to the first page of Preliminaries.


text:
Formal Logic/Sentential Logic/End of Sentential Logic

End of Sentential Logic A Sub-Book of Formal Logic

Places to go
 * Forward to the first page of Predicate Logic.

 * Backward to the last page of Sentential Logic.

 * Further back to the first page of Sentential Logic.


text:
Formal Logic/Predicate Logic/Start of Predicate Logic

Start of Predicate Logic A Sub-Book of Formal Logic

Places to go
 * Forward to the first page of Predicate Logic.

 * Backward to the last page of Sentential Logic.

 * Further back to the first page of Sentential Logic.


text:
Template:Sth

 Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec

title: Template:Sth


text:
Cookbook talk:Sushi Rice

it is important tu use double the amount of water then rice, to ensure that sushi nori can be rolled!

Sake?
Several recipes call for sake. Is this a bad idea? Jade Knight (talk) 14:16, 5 June 2008 (UTC)
 * Someone has removed sake from this recipe a while ago. I've put it back. Don't see anything wrong with the idea, especially since it's optional here. --X-Man (discuss • contribs) 11:50, 16 January 2011 (UTC)

Huge Unit Problem!
There's something wrong with the rice measurement. 1.5 cups does not equal 200 ml! Which measure is correct? The 1.5 cups or the 200 ml?

200 ml is about 0.85 cups

Measurement Issues
I've just altered this article to fix the problems with the incorrect measurements. I've also used traditional Japanese and metric measurements to reflect the Japanese origins of this recipe. Yukenoujo (talk) 00:19, 9 June 2009 (GMT)

Amount of water
The amount of water in this recipe seems to have been fluctuating, and the edit summaries in the history are not helpful. In March 2010, I cooked sushi rice according to the then-latest version of the recipe (with 400 mL of water), and that was successful. Over the course of 2010, the amount of water changed to 350 mL, then to 300 mL , and finally to 320 mL. In January 2011, I cooked it again according to the newest revision, which this time called for 320 mL of water, and it was clearly not enough. I've changed the amount of water back to 400 mL now, since this worked for me and 320 mL didn't. The amounts of sugar and salt have been fluctuating, too, see difference between March 2010 and now. I've changed them to the somewhat more precise older versions. --X-Man (discuss • contribs) 15:58, 13 February 2011 (UTC)

title: Cookbook talk:Sushi Rice