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Division by 0 … does it exist?

Let’s get a calculator and as it does not let divide by 0, we’ll try with numbers getting closer to 0.

Divide 1 by the following numbers: 0.1; 0.01; 0.001; 0.0001.

If you are lazy, just believe that the results gave: 10; 100; 1000; 10000.

So the closer to 0 we get, the more that division grows, so I can say that dividing a number by 0 gives ∞?

WRONG!

It would be too simple if it were so. For we only analyze the numbers close to 0 on the positive side. Now let’s approach them by the negative numbers.

Divide 1 by the following numbers: -0.1 -0.01; -0.001; -0.0001.

If you are lazy, just believe the results gave: -10; -100; -1000; -10000.

In both directions, we are equally close to 0, but in one of them we are going to + ∞ and in the other to -∞. So, exactly at 0, the result should be + ∞ and -∞ at the same time.

So dividing a number by 0 does not make sense!

The graph represents how the result of the division advances to + ∞ and -∞ as we approach point 0.