I just confused myself trying explain "infinity" to my daughter.
Infinity and a half is infinity. Check.
Half of infinity is infinity. Check.
Infinity minus half infinity is...what?
I get that $\infty-\infty$ is indeterminate, but Inf*(1-0.5) is obviously infinity. So I guess factoring out infinities is a no-go. That's fine. What about taking the limit?
$$\lim_{x\to\infty} x - 0.5x=\infty$$
Is that right? If it is, why is that not equivalent to $\infty-0.5\infty$?