# What is 1 divided by 0?

$\frac 10 \neq \infty$

Some say 1 divided by 0 is infinity. They argue that when a number is divided by smaller number the result is bigger number. And if we divide a number with a very very very small number it will give a very very very big number. According to them zero is a very very very small number therefore 1 divided by 0 will give infinity (a very very very big number). Is that true? NO!

While it is true that when a number is divided by smaller number the result is bigger number. Zero is zero. It's not an infinitely small number! It's nothing.

In maths, we know that

if $\frac a b = c$ , then $a = b \times c$ in that's true for $b \neq 0$

For $ b = 0 $, in the above equation, what is the value of c such that $ 0 \times c = a$?

There is no such number that when multiplied by zero will produce somethings. Any real number multiplied by zero will produce zero!

What is 1 divided by 0 then? It's undefined!

But for a very small number $h, \frac 1h = \infty $

$ \lim_{h \to 0} \frac 1 h = \infty $

Note that $h \neq 0$!

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