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Math Help - how to write z=x^n in terms of first order peanos aritmetic?

  1. #1
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    how to write z=x^n in terms of first order peanos aritmetic?

    i just want to kknow how do u write x^n in first order lang?
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  2. #2
    MHF Contributor
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    It's possible, but not trivial. The idea is to construct a sequence 1, x, x^2, ..., x^n and encode it in a single number. Encoding of sequences and operations on them can be done using Gödel's beta-function. See Definition 3 the following on this page (one of the first Google results for "exponentiation Peano Arithmetic").

    In general, every computable function is representable by a formula in Peano Arithmetic.
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