(adsbygoogle = window.adsbygoogle || []).push({}); Use of the term "pair" vs "ordered pair"

Why is it that authors use the term "pair" and "ordered pair" interchangeably and, maybe I'm mistaken, a little imprecisely? For example, in listing the field axioms, the language "for every pair x and y" is usually used. However, surly the author means "for every ordered pair x and y", otherwise, there is no need for the axiom of commutativity (neither for addition nor multiplication). Just something that has been bothering me.

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# Use of the term pair vs ordered pair

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