Changes

===Note 14===

===Note 14===

Table&nbsp;5 sums up the facts of the physical situation at equilibrium.  If we let <math>\mathbf{B} = \{ \mathrm{note}, \mathrm{rest} \} = \{ \mathrm{moving}, \mathrm{steady} \} = \{ \mathrm{charged}, \mathrm{resting} \},</math> or whatever candidates you pick for the 2-membered set in question, the Table shows a function <math>f : \mathbf{B} \times \mathbf{B} \to \mathbf{B},</math> where <math>f(x, y) = (x, y) = \operatorname{XOR}(x, y).\!</math>

Table&nbsp;5 sums up the facts of the physical situation at equilibrium.  If we let <math>\mathbf{B} = \{ \mathrm{charged}, \mathrm{resting} \} = \{ \mathrm{moving}, \mathrm{steady} \} = \{ \mathrm{note}, \mathrm{rest} \},</math> or whatever candidates you pick for the 2-membered set in question, the Table shows a function <math>f : \mathbf{B} \times \mathbf{B} \to \mathbf{B},</math> where <math>f(x, y) = (x, y) = \operatorname{XOR}(x, y).\!</math>

<pre>

<pre>

| resting | resting | charged |

| resting | resting | charged |

o---------o---------o---------o

o---------o---------o---------o

There are two ways that this physical function

There are two ways that this physical function might be taken to represent a logical function:

might be taken to represent a logical function:

1.  If we make the identifications:

*<p>If we make the identifications:</p><p><math>\mathrm{charged} = \mathrm{true}\ (= \mathrm{indicated}),\!</math></p><p><math>\mathrm{resting} = \mathrm{false}\ (= \mathrm{otherwise}),\!</math></p><p>then the physical function <math>f : \mathbf{B} \times \mathbf{B} \to \mathbf{B}</math> is tantamount to the logical function that is commonly known as ''logical equivalence'', or just plain ''equality'':</p>

    charged = true   (= indicated),

    resting = false (= otherwise),

    then the physical function f : B x B -> B

    is tantamount to the logical function that

    is commonly known as "logical equivalence",

    or just plain "equality":

     Table 6.  Equality Function

     Table 6.  Equality Function

     o---------o---------o---------o

     o---------o---------o---------o

     | false  | false  | true    |

     | false  | false  | true    |

     o---------o---------o---------o

     o---------o---------o---------o

2.  If we make the identifications:

2.  If we make the identifications: