Question

what is the reciprocal of infinity.​

Answer 1

In other words, ∞ is an undefined symbol. If you're using the projectively extended real line or the Riemann sphere, then the reciprocal of zero is infinity, and the reciprocal of infinity is zero. In other words, 1/0=∞ and 1/∞=0. (Note that the reciprocal of infinity is exactly zero, not infinitesimal.

Answer 2

1/0=∞ and 1/∞=0.

The reciprocal of infinity is exactly zero, not infinitesimal.