I have no idea what I'm attempting to get at with this one.

Anyway, the following must give a real number of some sort.

$\displaystyle \infty - 1 $

$\displaystyle \infty + 1 $

$\displaystyle (-\infty) - 1 $

$\displaystyle (-\infty) + 1 $

Thus, that real number will always be $\displaystyle \infty + 1 $ for an example.

But this now leads me to the conclusion, that any number can be made greater than infinity.

$\displaystyle \infty + 2 $

$\displaystyle \infty + 3 $

$\displaystyle \infty + \infty = (2)(\infty) $

What is going on at this end of the spectrum for the real number line?