What is 1 divided by 0?


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Let us assume for the sake of argument that there exist two real numbers ‘a’ and ‘b’ such that:

a/0 = b, a ≠ 0.
=> a = 0.b
=> a = 0 for any real number b, which is a contradiction. Hence, the form a/0 is ‘undefined’ when a≠ 0.

Now, we assume that a = 0. Then this implies that b.0 = 0, which holds identically for any real ‘b’ (1.0 = 0, 2.0 = 0 … and so on). As a result, the value of ‘b’ cannot be determined. And thus, division by zero is not allowed.

As such, the form “x = 0/0” is ‘indeterminate.’

A few more examples:

Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related.

12 divided by 6 is 2 because
6 times 2 is 12

12 divided by 0 is x would mean that
0 times x = 12

But no value would work for ‘x’ because 0 times any number is 0. So division by zero doesn’t work.

Another way to look at it is to imagine that there is a magic coin that takes up no space at all. How many such coins can you put into your coin box? Some people may say that the answer is “infinite”. But the real answer is – THERE IS NO ANSWER!

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