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Math Help - definition of a subfield

  1. #1
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    definition of a subfield

    in the definition of a subfield we have that it contains both the 0 and 1 elements.

    prove- this condition can be replaced by "it has at least 2 elements"

    I'm quite confused as to how to start this, if someone could give me a hint to get started that would be great.

    thanks for any help
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: definition of a subfield

    Quote Originally Posted by hmmmm View Post
    in the definition of a subfield we have that it contains both the 0 and 1 elements.

    prove- this condition can be replaced by "it has at least 2 elements"

    I'm quite confused as to how to start this, if someone could give me a hint to get started that would be great.

    thanks for any help
    Well, in a field you assume that 1\ne 0 and since every field has a multiplicative and additive identity.....
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