0/0 is positive infinity and negative infinity, which is why it's undefined. 1/0, for example, IS NOT ZERO. They teach you that in primary, but in primary, they also teach you that you can't subtract a bigger number from a smaller number. If you subtract 0 from 1 0 times you get... 1. The thing where the answer is every number is 0 to the power of zero.
Weird maths stuff
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Ah, Numberphile explains it better. Go search 'problems with zero' 'numberphile' or here's the url: https://www.youtube.com/watch?v=BRRolKTlF6Q&list=TL5oZTzf8Vx-0
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What does 0 divided by 0 equal?
0 divided by 0 is just another way of saying: what equals 0 when divided by 0? An the answer is, of course, every single number in existence. This means that 0 divided by 0 equals 1, 2, 3... Etc. using this, you could say that 1 = 2 = 3... Etc. weird things. Because of this, 0 divided by 0 is 'forbidden' and comes up with 'error' on a calculator.