Exponential of Sum/Real Numbers/Corollary

Corollary to Exponential of Sum: Real Numbers

Let $x, y \in \R$ be real numbers.

Let $\exp x$ be the exponential of $x$.

Then:

$\map \exp {x - y} = \dfrac {\exp x} {\exp y}$

Proof

By Exponential of Sum: Real Numbers:

$\map \exp {x - y} = \exp x \, \map \exp {-y}$

Although this article appears correct, it's inelegant. There has to be a better way of doing it. In particular: No real counterpart exists to link to You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by redesigning it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Improve}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

By Reciprocal of Complex Exponential:

$\dfrac 1 {\exp y} = \map \exp {-y}$

Combining these two, we obtain the result:

$\map \exp {x - y} = \dfrac {\exp x} {\exp y}$

$\blacksquare$