Changes

The briefest expression for logical truth is the empty word, usually denoted by <math>\varepsilon\!</math> or <math>\lambda\!</math> 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 "<math>((~))\!</math>", or, especially if operating in an algebraic context, by a simple "<math>1\!</math>".  Also when working in an algebraic mode, I use the plus sign "<math>+\!</math>" 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 <math>\varepsilon\!</math> or <math>\lambda\!</math> 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 "<math>((~))\!</math>", or, especially if operating in an algebraic context, by a simple "<math>1\!</math>".  Also when working in an algebraic mode, I use the plus sign "<math>+\!</math>" for exclusive disjunction.  Thus, we may express the following paraphrases of algebraic forms:

:{| cellpadding="4"

| ''A'' + ''B''

<p><math>\begin{matrix}

| =

x + y & = & (x, y)

| (''A'', ''B'')

\end{matrix}</math></p>

|}

One should be careful to observe that these last two expressions are not equivalent to the form (''A'',&nbsp;''B'',&nbsp;''C'').

 

It is important to note that the last expressions are not equivalent to the triple bracket expression <math>(x, y, z).\!</math>

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