Difficulties in Arithmetic with Infinity - Expii

One reason people often say "infinity is not a number, it's a concept" is that it's hard to reliably do arithmetic with it when you're talking about limits. You usually want to reason about ∞ in some context. For example, in the context of infinite limits, it's safe to say ∞+∞=∞, but ∞−∞ is ambiguous. We will elaborate on the difficulties when talking about indeterminate forms later on.