Can we divide by 0?

Algebra Level 2

No. of solutions of the equation 1/x = 1/0

One Infinitely many Two Zero

2 solutions

Nelson Mandela
Jul 26, 2015

There are no solutions because we cannot cross multiply. Moreover, 1/0 is not defined.

Thanks to Sudeep Salgia.

Firstly one cannot cross multiply by $0$ . Secondly even if that was possible then by that logic then the "Number of Solutions" would be $1$ and not $0$ .

Sudeep Salgia - 5 years, 10 months ago

By substitution, we can try zero for x and end with two equivalent forms. As the forms are equivalent, so are the values.

I suppose it depends on how we are considering the relation of equality.

Just trying to understand this one.

Peter Michael - 5 years, 10 months ago

I agree with Peter Michael. The fact that 1/0 is undefined doesn't mean it is not 1/0. When x=0 then 1/x equals 1/0, which is undefined. 1 solution. A=A, B=B, these are tautologies. 1/kumquat = 1/kumquat by the same logic. The fact that 1/kumquat has no meaning seems to me irrelevant.

wayne dill - 5 years, 9 months ago

Majed Kalaoun
Jul 19, 2017

$\dfrac{1}{x}=\dfrac{1}{0}$ . Cross multiplying, we get:

$\boxed{x=0}$

This isn't a solution, it's a report.

Blan Morrison - 3 years, 2 months ago

Can we divide by 0?

2 solutions

0 pending reports