Does $\frac {1}{∞} = 0$?

Question

Actually , I am not believing that $\frac {1}{∞} = \frac{0}{1}$ because simply $0 ≠ 1$ (we get this if we multiple numerator by denominator) , In the other hand it is very very very small , So I am confused

Answer 1

Since $\infty$ is not a number, asking what is the quotient of the division of $1$ by $\infty$ doesn't make sense.

Answer 2

In the extended complex plane (a.k.a the Riemann Sphere), the answer is yes.

Answer 3

In the Extended Real Numbers, it is common to adopt

$$\dfrac{c}{\infty} = \dfrac{c}{-\infty} = 0$$

See: https://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations