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, 15:30, 23 January 2008→Review and Transition: bind expressions with
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The briefest expression for logical truth is the empty word, usually denoted by ε or λ in formal languages, where it forms the identity element for concatenation. To make it visible in this text, I denote it by the equivalent expression "(())", or, especially if operating in an algebraic context, by a simple "1". Also when working in an algebraic mode, I use the plus sign "+" for exclusive disjunction. Thus, we may express the following paraphrases of algebraic forms:
The briefest expression for logical truth is the empty word, usually denoted by ε or λ in formal languages, where it forms the identity element for concatenation. To make it visible in this text, I denote it by the equivalent expression "(())", or, especially if operating in an algebraic context, by a simple "1". Also when working in an algebraic mode, I use the plus sign "+" for exclusive disjunction. Thus, we may express the following paraphrases of algebraic forms:
−:{|
+:{| cellpadding="4"
−| ''A'' + ''B'' || = || (''A'', ''B'')
+| ''A'' + ''B''
+| =
+| (''A'', ''B'')
|-
|-
−| ''A'' + ''B'' + ''C'' || = || ((''A'', ''B''), ''C'') || = || (''A'', (''B'', ''C''))
+| ''A'' + ''B'' + ''C''
+| =
+| ((''A'', ''B''), ''C'')
+| =
+| (''A'', (''B'', ''C''))
|}
|}
−One should be careful to observe that these last two expressions are not equivalent to the form (''A'', ''B'', ''C'').
+One should be careful to observe that these last two expressions are not equivalent to the form (''A'', ''B'', ''C'').
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