Why does dividing a number by zero not result in a value of zero?

So what'd be the answer?

So what'd be the answer?

Typical Asian parent mindset

Not a mathematician but I'd have thought that's a perfectly reasonable explanation. Maths is simply the result of a series of axioms that we decide on because of their use in achieving sensible results. If x/0 had any defined value, it would result in logical inconsistencies.

There is no answer.

So that answer in your opinion is correct?

If your answer is to ensure logical consistency then yeah, I guess so.

If x is a real number and you define it being divided by zero as zero:

$\frac{x}{0} = 0$
$x = 0$

Therefore it's inconsistent with the normal rules of arithmetic, that's why the value of $\frac{x}{0}$ is undefined.

I always thought of it in primary school terms.
If there are 6 sweets, and two people want them, they get three each.
If there are 6 sweets and no one wants them, then you can't say how many each person gets, because there are none, but you can't say they get no sweets each, because then the original 6 won't be given to anyone.
That makes less sense than I thought, but oh well.

Is it because zero has no value? or because it isn't divisible? or because anything multiplied by it equals zero?(I know that doesn't sound like the right answer) or because it is not consistent with division by other numbers?

Thanks in advance

Why would it, you can take 0 out of any real number an infinite number of times. Also dividing a number by zero does not equal infinity, or else you can prove absurd results like 2=0, it's clearly a nonsense operation.

It doesn't equal zero because as the denominator approaches 0, the result shoots to infinity.

$\frac{1}{10}=0.1$
$\frac{1}{1}=1$
$\frac{1}{0.1}=10$
$\frac{1}{0.01}=100$
$\frac{1}{0.001}=1000$

...and so on. As you can see, as you get closer and closer to 0 in the denominator the result goes up and up, so division by zero (even if it was possible) wouldn't be equal to 0 itself anyhow.

If division is the equal distribution of finite objects to a finite group then the distribution is zero in the case that there is no group. Why not just make an exception to the rules of arithmetic?

Why can't we do what they do with complex numbers and call it a 'second zero' or 'zero negative' or another appropriate name? The demonstration below describes how there is a kind of zero or absence derived from the calculation.

If division is the equal distribution of finite objects to a finite group then the distribution is zero in the case that there is no group. Why not just make an exception to the rules of arithmetic?

YESS! Thanks, makes sense now

Yeah, but that won't have anything to do with it, for example if I were able to take an infinite number of 2's out of a number, that doesn't necessarily mean dividing that by 2 won't result in a value of 2, no?

Good.

Also in regard to division by 0 equaling infinity; nope. Infinity is not a number therefore we cannot define division by 0 to be equal to it, therefore division by 0 is undefined.

If you have 0/0 then you might think that it either shoots up to infinity, or it simply equal to 1 because its a number divided by itself. For this reason, we cannot determine which one it is therefore it is indeterminate.

Which number can you take an infinite number of twos out of? If I have a number which gives me magical powers, why am I not a wizard?


Because it's something I made up rather than an actual mathematical object.