Chaining operators and relations: Difference between revisions
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When you have several terms with operators in between, some kind of associativity is normally implied, so that the expression can be evaluated as a sequence of binary operations: | When you have several terms with operators in between, some kind of associativity is normally implied, so that the expression can be evaluated as a sequence of binary operations: | ||
Revision as of 14:23, 14 July 2021
When you have several terms with operators in between, some kind of associativity is normally implied, so that the expression can be evaluated as a sequence of binary operations:
\[ a \cdot b \cdot c = (a \cdot b) \cdot c \]
That isn't usually the case when terms are joined with relation symbols[1][2]:
Let \(a=1\), \(b=2\), \(c=3\).
\( (a \lt b) \lt c = \text{True} \lt c \)
It doesn't make sense to evaluate this as a sequence of binary operations. Instead, a chain of \(n\) relations could be interpreted as a set of \(n\) statements:
\[ a \lt b \lt c \iff (a \lt b) \wedge (b \lt c) \]
