Question

Prive that 1/0 = infinity

Answer 1

1/0 is undefined.

So lets consider a real life situation. Lets say Mr.Mark is buying an apple. let it be a magic apple with infinite life(please assume as a one which does not decay). He wants to eat it for two days. So

1/0.5=2 days. He eats half an apple a day. If he wants to eat it for three days,

1/0.333=3 days. The amount of apple he gets to eat is reduced. Lets reduce it further.

1/0.1=10 days. Further more..

1/0.05=20 days. Save apple for even more no. of days..

1/0.0001=1000 days.

1/0.0000001=1000000 days. So,

1/0.00…..001=100……00 days. And it goes on. Which means

1/0=∞. So, literally we can 1/0=∞. But lets us consider these answers..

1/-0.5=-2(don’t ask me how there can be negative amount of apples, please)

1/-0.1=-10

1/-0.0001=-1000 and so

1/-0.00……001=-100……00. Which means,

1/-0=-∞

We all know that zero is unbiased, which means there is no such thing as -0 and +0. This makes us conclude that -∞=∞. Which is not true. So the above observations 1/0=∞ and 1/-0=-∞ are wrong in terms of strict math. So the mathematicians call it UNDEFINED.

Lets have a deep look in mathematical terms. See the 1/x curve.


At zero we have two points. The one from right approaches positive infinity and the one from left approaches negative infinity. We can’t have two answers for a division operation, which is why division by zero is ruled out.

In terms of calculus

limx→0+1x=+∞andlimx→0+1x=+∞and

limx→0−1x=−∞limx→0−1x=−∞

The answer should be the same if we approach from either side of the limit. Here, the one sided limits are different which makes it unfit for the standard framework of math. And so 1/0 is UNDEFINED.