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

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- March 4th 2009, 05:31 PMthehollow89predicate logic
*“Exponentiation on reals has no left identity.” What does this mean exactly?*

- March 6th 2009, 01:06 AMGrandadIdentity element
Hello thehollow89Exponentiation on reals takes a real number, , and raises a base, , say, to the power of . So, using notation, exponentiation can be defined as the binary operation:

.

A left identity is an element in the domain of , such that in the domain.

So to say that exponentiation on reals has no left identity is to say that there is no real number for which .

Grandad