predicate logic

Hello thehollow89

Quote:

Originally Posted by thehollow89

“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