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Math Help - What does "Up to Isomorphism" mean?

  1. #1
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    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!!
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  2. #2
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    Quote Originally Posted by buri View Post
    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
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  3. #3
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    Quote Originally Posted by undefined View Post
    ...
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  4. #4
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by buri View Post
    ...
    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.
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  5. #5
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    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
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