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Math Help - proof about 0

  1. #1
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    proof about 0

    Hello people of MHF. Apostol states as the 4th field axiom (of real numbers): "Given any two real numbers x and y there exists z such that x+z = y. z is denoted y-x. The number x-x will be designated by 0". How do I prove 0 doesn't depend on x? Any help is appreciated.
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  2. #2
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    Re: proof about 0

    if it's true for all x it doesn't depend on x
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  3. #3
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    Re: proof about 0

    The proof depends on other axioms, and since Apostol's definition of subtraction is rather non-standard, it is probably necessary to see these other axioms.
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