The sum of negative infinity and positive infinity is zero after all.

No, you can't say that. It's not meaningful to talk about the sum of negative infinity and positive infinity.

Suppose you have a hotel with an infinite number of rooms. An infinite number of guests arrive and check into these rooms, starting with Room 1, then Room 2, Room 3, etc.

The next day, the guest in Room 1 wants to stay, but every other guest checks out, starting with Room 2, then Room 3, Room 4, etc.

An infinite number of guests arrived, and an infinite number of guests left, but Room 1 is still occupied. So does infinity minus infinity equal one?

Assuming ∞ - ∞ = 0...

Let's add 1 to both sides...

∞ - ∞ + 1 = 0 + 1

∞ + 1 = ∞ and 0 + 1 = 1...Simplify...

∞ - ∞ = 1

Interesting, infinity minus infinity can be equal to any real number...all numbers. So infinity minus infinity is still infinity.