No... The easiest example off the top of my head is the following: the limit of e^x as x→∞ = ∞. The limit of e^x as x→-∞ = 0. If +∞ = -∞, then the two limits would be equal, and no one is arguing the possibility of 0 = ∞.
If you then want to ask if 0 does indeed equal infinity, we could just use a similar argument: the the limit of e^x as x→0 = 1. By definition, 1 (a finite number) cannot equal infinity.
Many people would rather die than think; in fact, most do. - Bertrand Russell