My question is $\frac{0}{0}*0=?$ I think it should be zero. Beause $\frac00$ can be any number (both real or imaginary). And I think any number multiplied by $0$ should be $0$. I know the proof like this: x*0=y*0 so (0/0)=(x/y) Thus (x/y) can be any number. If this is a common question, please do not downvote?
2026-04-11 22:02:13.1775944933
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Zero: Dividing and multiplying
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My question is (0/0)*0=?
It's not defined because $0/0$ is not defined
Beause (0/0) is any number
No it's not.
And any $\color{red}{\text{number}}$ multiplied by 0 should be 0
True, but as said before, $0/0$ is not a number.
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Common problem in mathematics to think about expressions as computational steps which you carry out in your head, so you can talk about steps being undefined. Mathematics is all about statements and the rules which connect these statements. When you write $\frac{0}{0}$ you say "the number which is 0 multiplied by the inverse of 0" at this instant you introduced an object the existence of which you have not proven (the inverse of zero) so your question can be rephrased as:
"Assuming the existence of the inverse of 0 and denoting it with $\frac{1}{0}$ what $\frac{0}{0}0$ is equal to?" Since your assumption leads to contradiction the answer is everything.
It is not $0$. And it is not different from $0$. It is just meaningless.