What is inifinity ∞ ?

What is infinity ∞ ? Is it prexisting or not countable with respect to defination. If we consider infinity ∞ is something in which we can not add anything or remove anything then its justify below equations are wrong with respect to logic and understanding.

∞ + 1 = ∞ (1 = ∞ – ∞ = 0)

∞ – 1 = ∞ (-1 = ∞ – ∞ = 0)

1 / ∞ = 0 (1 = ∞ * 0 = 0)

1 / 0 = ∞ (1 = 0 * ∞ = 0)

Suggestions and thoughts are most welcome.