# Chaining operators and relations

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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:

$a \cdot b \cdot c = (a \cdot b) \cdot c$

That isn't usually the case when terms are joined with relation symbols[1][2]:

Let $$a=1$$, $$b=2$$, $$c=3$$.

$$(a \lt b) \lt c = \text{True} \lt c$$

Doesn't make sense!

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:

$a \lt b \lt c \iff (a \lt b) \wedge (b \lt c)$