"Up to Isomorphism"?

Up to isomorphism” is a phrase that seems to get thrown around a lot without ever being explained. Simply put, we say two groups (or any other algebraic structures) are the same “up to isomorphism” if they’re isomorphic! In other words, they share the exact same structure and therefore they are essentially indistinguishable. Hence we consider them to be one and the same! But, you see, we mathematicians are very precise, and so we really don't like to use the word “same." Instead we prefer to say “same up to isomorphism.” Voila! 

Related Posts

Completing a Metric Space, Intuitively

The Back Pocket

Why are Noetherian Rings Special?

The Back Pocket

Motivation for the Tensor Product

The Back Pocket
Leave a comment!