You can for sure have infinite numbers plus one, or divided by two.

Those kind of numbers are called transfinite numbers (ω, ℵₒ, m)

They are not finite, just not absolutely infinite (∞).

But a transfinite number t + 1 is, well, (t + 1) and t / 2 is (t / 2)

Which is not the case for ∞ + 1 or ∞ / 2 which both are still ∞

Maybe I shouldn't go into transfinite numbers in eli5...