I've always thought that the number zero, has a concept, was a remarkable achievement. Here's a detailed and technical explanation as to why we can't divide by 0.

**The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction.**

To begin with, how do we define *division*? The ratio *r* of two numbers *a* and *b*:

*r=a/b*

is that number *r* that satisfies

Well, if *b=0*, i.e., we are trying to divide by zero, we have to find a number *r* such that

*r*0=a*. (1)

*r*0=0*

for all numbers *r*, and so unless *a=0* there is no solution of equation (1).

Now you could say that *r=infinity* satisfies (1). That's a common way of putting things, but what's infinity? It is not a number! Why not? Because if we treated it like a number we'd run into contradictions. Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then

*infinity = infinity+1 = infinity + 2*

which would imply that 1 equals 2 if infinity was a number. That in turn would imply that all integers are equal, for example, and our whole number system would collapse.

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