# predicate logic

• Mar 4th 2009, 06:31 PM
thehollow89
predicate logic
“Exponentiation on reals has no left identity.” What does this mean exactly?
• Mar 6th 2009, 02:06 AM
Identity element
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 $i^x = x, \forall x \in \mathbb{R}$.