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Is zero divisible by zero?
(lemmy.world)
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this post was submitted on 08 Oct 2023
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Zero divided by zero is undefined. In that it literally does not meet the definition of division (from a mathematical perspective.)
This is a bit tricky because the reason that 0/0 is undefined is separate from why any other number divided by zero is undefined.
If I divide 6 by 0, there's no number I can multiply by zero to get back to 6. Since I can't get back to the 6, this is undefined.
If I divide 6 by 2, I get 3. And I can multiply 2 by 3 to get 6. Now it's genuinely important that there is no other number I can multiply 2 by to get 6. There has to be a single unique result for both the division and the going back via multiplication.
Now, if we assume 0/0 = 1, that is fine. And I can multiply 1 times 0 to get back to 0. Checks out so far. However, 1 isn't unique in getting back to 0. If I try 5 x 0, I get 0. Which, by the rules of division should mean that 0/0 = 5. Which clearly it wouldn't.
So zero divided by zero is undefined because there is an infinite amount of numbers that would get me back to zero.