1/infinity Does NOT Equal -1/infinity!
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Ok
Let's hope Google catches this one.
As X approaches ∞, 1/X approaches 0. Thus 1/∞ is technically 0. 1/0 = ±∞ based on whether you are approaching from the positive or negative side.
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For it is true that, (1/infinity)^-1 is infinity/1
While (-1/infinity)^-1 is -infinity/1
They differ.