"15" is an isomorphism of 15, so why shouldn't "15" == 15?
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Anonymous2015-03-21 20:45
The existence of an isomorphism between two structures doesn't imply their equality, Undergrad-kun.
"15" is not ``an isomorphism of 15'' (that doesn't even make sense), though there exists an isomorphism between the set of strings composed only by digits between 0 and 9 and the set of natural numbers. If you had some way of creating this function and calling it f, the proper way of comparing these two is creating an isomorphism operator. Let's call it ~(f). In that case, you'd want your language to evaluate "15" ~(f) 15 as true, yet it is never true that "15" == 15.