Question

What is infinite minus infinite?

Answer 1

If we assume
∞ - ∞ = 0

∞ - ∞ + 1 = 0 + 1

Since ∞ + 1 = ∞ and 0 + 1 = 1, then we are going to simplify both parts of the equation: 

∞ - ∞ = 1 (but not possible)

Let's prove this another way. Again, assuming this is true: 

∞ - ∞ = 0

Since we know that ∞ = ∞ + ∞, then we get: 

(∞ + ∞) - ∞ = 0

∞ + ∞ - ∞ = 0

Since we assumed ∞ - ∞ = 0, then
∞ + 0 = 0

∞ = 0

This is obviously incorrect, so :
∞ - ∞ ≠ 0

∴∞ - ∞ = undefined

Let's say :
∞ - ∞ = n

Since we know that ∞ = ∞ + ∞,  we get: 

(∞ + ∞) - ∞ = n

Which is equal to: 

∞ + ∞ - ∞ = n

Since we already assumed ∞ - ∞ = n,
∴∞ + n = n

∞ = 0

So

∞ - ∞ ≠ n

Specifically, we can again conclude that

∞ - ∞ = undefined

Answer 2

Suppose I have infinite number of rooms numbered as 1, 2, 3 and so on
If I give all the odd numbered rooms, then also i have infinite number of rooms.
we conclude that ∞-∞=∞
if i give all of them, then i will have 0
∞-∞=0
if i give all the room except for the first 10, then i will have 10 rooms
so ∞-∞=10
since ∞≠0≠10
so ∞-∞ is not defined