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Math Help - How to write this in formal language

  1. #1
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    How to write this in formal language

    The set of even natural numbers not expressible as the sum of two primes is finite.

    How do you write even numbers in formal language? i'm talking about peanos first order.
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  2. #2
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    n is even iff \exists m\,(2m=n)

    n is expressible as the sum of two primes iff \exists m_1\exists m_2\,(\mbox{prime}(m_1)\land \mbox{prime}(m_2)\land n = m_1+m_2)

    The set of natural numbers satisfying a property P is finite iff \exists n\forall m\,(P(m)\to m<n)

    Try expanding prime(m).
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  3. #3
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    im sorry what do u mean by expand?

    do u mean write them in abberviations ?
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  4. #4
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    I meant, try writing prime(m) in the language of Peano Arithmetic.
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  5. #5
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    yeah it make sennse i got it thanks xD
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