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Math Help - predicate logic

  1. #1
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    predicate logic

    “Exponentiation on reals has no left identity.” What does this mean exactly?
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  2. #2
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    Identity element

    Hello thehollow89
    Quote Originally Posted by thehollow89 View Post
    “Exponentiation on reals has no left identity.” What does this mean exactly?
    Exponentiation on reals takes a real number, x, and raises a base, a, say, to the power of x. So, using \circ notation, exponentiation can be defined as the binary operation:

    a\circ x  = a^x.

    A left identity is an element i in the domain of
    \circ, such that i \circ x = x, \forall x in the domain.

    So to say that exponentiation on reals has no left identity is to say that there is no real number i for which i^x = x, \forall x \in \mathbb{R}.

    Grandad
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