- #1

ProfuselyQuarky

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So I have two sets, call it ##A## and ##B##. I also have a function ##f:A\rightarrow B##. By themselves, it does not matter (or at the very least make sense) to think of ##A## and ##B## as, say, groups (I'm not really thinking exclusively about groups, just as an example). For that matter, it doesn't make any sense to think that ##f## is group homomorphism.

I started to briefly learn about rings and how every field is a ring, every ring is a group, which makes every field a group, too. So what if sets ##A## and ##B## have binary operations? In this case, they might be groups! If ##

A## and ##B## are, indeed, groups, then we can question whether ##f## is group homomorphism, too.

Whether sets and functions have more structure or not is completely dependent on the context which is being spoken of. To me, that just doesn't sound right. Shouldn't there be a precise way of determining whether a set or function has more structure or not? Is there?

I started to briefly learn about rings and how every field is a ring, every ring is a group, which makes every field a group, too. So what if sets ##A## and ##B## have binary operations? In this case, they might be groups! If ##

A## and ##B## are, indeed, groups, then we can question whether ##f## is group homomorphism, too.

Whether sets and functions have more structure or not is completely dependent on the context which is being spoken of. To me, that just doesn't sound right. Shouldn't there be a precise way of determining whether a set or function has more structure or not? Is there?

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