This applies to any numbers being divided by 0 really. In all honesty, wouldn’t 0 divided by anything just be 0? There was nothing there to divide in the first place, so why expect there to magically be a resulting number when you divide nothing?
In: Mathematics
I think you’re right, it should just be zero. A lot of the explanations seem needlessly complicated, and unnecessary. If it’s an “undefined infinite number” that doesn’t really exist right? So if existence = 1 but you remove the equation, you end up with zero. Math is meat
The answer to a division problem is the result of distribution, if you have nothing to distribute and nothing to give to, the action cannot be performed so you don’t have a result
For example: if you try to see what happens after giving 0 cookies to 0 friends, you can’t because the act of giving (dividing) has not been performed
If you divide by almost zero on the positive side you approach positive infinity.
1/.0001
1/.000001
1/.0000000001
And so on.
If you divide by almost zero on the negative side you approach negative infinity.
Since the left and right side converge to different numbers, you can’t extrapolate this to dividing by exactly zero so it’s undefined.
If they approached the same number you could.
Source: calculus
I like the approach of seeing division as reverse multiplication. When I ask what 12/3 is, I’m really asking “what number times 3 gives me 12?”. In this case, 12/3=4 precisely because 4×3=12.
The nice thing here is that in any case where you’re dividing by a non-zero number, the result will be unique, so we can invent a number like 17/31 as “the number that, when multiplied by 31, produces 17”.
If I asked what 1/0 is, I’m looking to find a number that when multiplied by 0 gives 1. This doesn’t work because 0 times any number is 0. There is not a single number that will qualify to be 1/0, so it’s undefined. The same logic can work for any non-zero number divided by 0. But what about 0/0? After all, any number times 0 is 0. And that’s the problem with 0/0. Because any number can be multiplied by 0 to get 0 (3×0=0, 15.9×0=0, -2×0=0, etc), we lose the uniqueness of division I mentioned before. So we leave 0/0 undefined as well.
Here is the explanation I got that made a lot of sense to me: if we say 30/5 = 6, how do we check? We multiply both sides by 5: 30 = 5*6=30. True. Now let’s try with dividing by zero: 30/0 = a. No matter what value we pick for a, when we multiply we always get 30=0. That can never be true.
The only exception is 0/0. In this case, we could pick *any* value for a in the equation 0/0=a. When we multiply both sides, we always get 0=0, which is why this form is called indeterminate: it can be any value, we can’t determine which
Just reverse the question you’re posing to see the problem. Let’s just pick the number 2 to work with;
2 / 0 = ? , can be algebraically rewritten as 0 x ? = 2. The problem is, no real number works for “?”. 0 multiplied by *anything* is equal to zero. So when we put that logic in reverse, we run into a problem where *anything* divided by zero = ???? [nothing mathematically possible/relevant]
So when you divide x by y, the answer is the equal amount each of y people will get that will add up to x.
So when you divide 0 by some non zero number each person gets 0, and that obviously adds up to 0. Satisfying the condition.
Now when you are dividing 0(or any number) by 0, you are dividing it between 0 people, ie you aren’t really dividing. So there isn’t any answer, or it’s indeterminate.
No matter how many times you divide nothing by nothing you still have nothing.
No matter how many times you divide nothing by nothing, you still have nothing…
No matter how many times you divide nothing by nothing, you still have nothing…
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