Two sets are equal iff they contain the same elements.(adsbygoogle = window.adsbygoogle || []).push({});

I would argue that two sets that have the same elements are identical as well as equal and that there is a difference between identity and equality. In general {2,3}={3,2} if neither set is defined to be ordered. However obviously {5} [tex]\neq[/tex] {2,3}. Under addition 2+3=5 but I would argue this is an equality but not an identity. I'm not sure distinction is really observed in mathematics.

EDIT: Two formulas in a formal language are equivalent iff one can be substituted for the other in a sentence. I don't think there is a necessary distinction between 'equal' and 'equivalent' unless you consider 'identical' and 'equal' to be synonymous. If you do, than this would lead to a lot of problems with the usual descriptions of equations. 3+2=5, but the two formulas are not identical. If they were, we wouldn't need to solve equations.

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# Equality and identity of sets

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