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Why does 0/0 ≠ 0? Part 2

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>Essentially if you multiply 0/0 by 2 it will equal 0/0 suggesting that its product is a zero value.

What you're saying is

* **If** 0/0 is defined
* and **If** 2 times 0/0 is 0/0
* **Then** 0/0 must be zero

And I agree with you. But the **first if isn't true** at all, so the entire statement doesn't make sense. Compare this to

* **If** all celestial bodies are flat
* and **If** you see a round moon
* **Then** the moon must be a disc

It looks like you tried to include an image but it doesn't show for some reason
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If you allow for division by 0, you can end up with all kinds of mathematical proofs such that 1=2.
Just don't ever divide by 0

If you want I can show an example of maths getting fucked when you divide by zero, just say the word
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Look, to **divide** by a number *means* to **multiply by the multiplicative inverse** of that number. Or, in other words, division by *x* is multiplication by a number *y* such that *xy* = 1.

Now, clearly, zero does not have a multiplicative inverse, i.e., there is no such number *y* for which 0*y* = 1. Therefore, division by zero is nonsensical by the very definition of what division is. You can try as you might, but there is no way to escape this fact.
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When you are trying to give a value to 0/0, you are essentially asking "What number, when multiplied by 0, gives us 0?". The answer is every number.
So 0/0 would be equal to every real number, which means that every number would be equal to each other, which doesn't make any sense.

There is also another reason as to why 0/0 is undefined.
It's a conflict between 2 rules:
0/a = 0 and
a/0 is undefined, for any positive value of a.
When you combine these 2 rules, you would end up with something that is both 0 and undefined. Again, that makes zero sense.
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Look at it this way. The rationals are defined as all pairs of whole numbers ie a/b = (a,b) where b is non-zero under a certain equivalence relation. This means that we consider two pairs (a,b) and (c,d) to be ‘equal’ when ad=bc. If we add a pair (0,0) to the mix we would find that (0,0) = (a,b) for any (a,b) so any fraction would be equal to 0/0 which would not work. That is why we don’t define division by zero.
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