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.
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