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# Why can't I divide by 0?

The short answer to this is because 0 does not have an inverse. Division is defined by multiplication, for example, if you want to divide by 2, you can multiply by a half (the inverse of 2):
30 × 0.5 = 15
 Algebraically, when a = c then a = bc b
 For 1 = x, there is no value for x where 1 = 0 × x because multiplying by zero gives 0 as a result. 0
The number zero does not have an inverse so you cannot divide by it but I will discuss other ideas...

## Now things get odd...

If you define division as a series of subtractions, it seems to be logical that dividing by zero equals infinity since you are subtracting 0 an infinite amount of times. The problem is with the definition. Here is why 1/0 does not equal infinity:
 If 1 = ∞ then 0
1 = 0 × ∞ but anything multiplied by 0 is 0.
Even if you considered that this does equal 1, it is shown to be false when you try it with other numbers:
 If 5 = ∞ then 5 = 0 × ∞ 0
this would imply that multiplying 0 with infinity equals an infinite amount of numbers.
Even if you could "trick" equations by having something say divided by n-n, then you may get some very strange results.

Now let's look at a graph of 1/0:

As you can see, approaching 0 from the right makes the result grow towards infinity BUT if you approach 0 from the left, the result approaches negative infinity. There is no number in the middle that the result could be.

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