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.
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.