# Question #0dd3d

Jul 24, 2016

There is no ambiguity in the definition of number $1$ as $\frac{1}{\text{infinity}} \ne 0$.

#### Explanation:

Division by $\infty$ needs to be dealt with very carefully.

First of all we must appreciate what exactly is $\infty$

It is a sufficiently large number, as such may not be unique. Therefore,

1. When a number is divided by $\infty$, the result is an arbitrarily chosen number $\epsilon$ which is very close to zero, but not exactly equal to zero.
2. The limit of number $\frac{1}{n}$ as $n$ tends to infinity is zero; but $\frac{1}{\text{infinity}} \ne 0$.