Thread: What does "Up to Isomorphism" mean?

I was reading the final chapter in Spivak's Calculus and it says:

There is a complete ordered field and, up to isomorphism, only one complete ordered field.

I know what an isomorphism is and what it means when things are isomorphic. But I don't know what he means when it says "UP to..". I've also read things like this when talking of homotopy...

Any help is appreciated!!

Originally Posted by buri

I was reading the final chapter in Spivak's Calculus and it says:

There is a complete ordered field and, up to isomorphism, only one complete ordered field.

I know what an isomorphism is and what it means when things are isomorphic. But I don't know what he means when it says "UP to..". I've also read things like this when talking of homotopy...

Any help is appreciated!!

up to

Originally Posted by undefined

up to

...

Originally Posted by buri

...

What do you mean by "..."? Maybe the coloration didn't stand out enough and you didn't see that there was a link to click? It goes to a Wikipedia article.

Whoops, sorry. I just had other people give me answers like 'it just means up to'..so I thought this was another one of those. Really sorry! Weird I had searched the phrase in google, but nothing came out :S Thanks for the link