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Revision as of 17:07, 15 January 2009
, 17:07, 15 January 2009→Propositions and Sentences: delete reconciled changes
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The "indicator function" or the "characteristic function" of a set Q c X,
−written "f_Q", is the map from X to the boolean domain %B% = {%0%, %1%}
−that is defined in the following ways:
−1. Considered in its extensional form, f_Q is the subset of X x %B%
− that is given by the following formula:
− f_Q = {<x, b> in X x %B% : b <=> x in Q}.
−2. Considered in its functional form, f_Q is the map from X to %B%
− that is given by the following condition:
− f_Q (x) <=> x in Q.
−
<pre>
<pre>
−The "fibers" of truth and falsity under a proposition f : X -> %B%
The "fibers" of truth and falsity under a proposition f : X -> %B%
are subsets of X that are variously described as follows:
are subsets of X that are variously described as follows:
