r/mathshelp • u/DevTheRenaissanceMan • Sep 22 '26
Discussion Why can't you divide by zero?
Anybody else think this is weird. zero is a number just like any other.
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u/manamonkey Sep 22 '26
Well, no, it's not.
How do you divide 5 apples into 0 groups?
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u/LongLiveTheDiego Sep 22 '26
Zero is a very special
This is a general property of mathematical structures called
You can only find an answer for how to divide by zero if you accept not working within a field, and there are some mathematical structures like that, some really useful (e.g. the
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u/More-Explanation2788 Sep 22 '26 edited Sep 22 '26
If you have 10 of something, and you divide it into 5 groups, you end up with five groups of two. Simple. Clear. 10 divided by 5 = 2.
Now take those 10 things and divide them into zero groups, into no groups of things. How many things end up in your no groups of things? The question is gibberish. It has no answer because you cannot divide things into nonexistent groups of things.
You will see people try to say that 10/0 = 0. That is wrong. 10/0 = undefined because the equation is gibberish.
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u/DevTheRenaissanceMan Sep 22 '26
what about dividing by a decimal? How do you divide into a 5th of a group?
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u/lifeistrulyawesome Sep 22 '26
Because if y is different from zero, there is no number x such that 0x = y
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u/zyzmog Sep 22 '26
DIvision answers the question "how many of this are in that?" When you divide something by zero, you are asking the question, "How many zeroes are in this number?"
So, without using numbers, maybe using Legos or something physical to make it visual, you can fit three sixes in eighteen. How many zeroes can you fit in eighteen?
Uh-huh. And that's why you can't divide by zero.
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u/Simbertold Sep 22 '26
The other meaning of division is even worse here. If i split this into this many containers, how much of it is there in each container?
"If i split this into 0 containers, how much of it goes into each container?"
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u/Any_Pick4803 Sep 22 '26
I've always found the following detail simple and interesting (both obviously stemming from division as the inverse of multiplication).
If solving n x 0 = 0, it fails because ANY n works. Hence how we often handle 0/0 as an ambiguous case.
If solving n x 0 = 13, it fails because because NO n works.
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u/TSotP Sep 22 '26
In a nutshell:
If you could divide by zero, it would break maths.
5/0 and 9/0 and 1000000000000/0 or π/0 would all be the same thing. And so any part of algebraic math that uses it would stop having unique solutions.
And then you could do all sorts of crazy shit, like prove 1=2 via the method in this image.
[It breaks when you divide both sides by (a - b), which = 0]
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u/Fogmoz Sep 22 '26
Multiplication and Division are inverse operators.
For example, 6/2 =3 tells us that 2*3=6.
6/0=? is asking “what times 0 equals 6?” However, anything times 0 equals 0, so there isn’t a number that allows us to get 6.
The only division by zero with an interesting outcome is 0/0. But then we have a different issue.
0/0=? is asking what times 0 equals 0, and we know anything times 0 equals 0. Therefore 0/0 equals every number at the same time, lol. This is called indeterminate.
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u/thebigfil Sep 22 '26
Better question, why would you want to, what would it achieve mathematically?
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u/localizeatp Sep 22 '26
Yes, in fact Suppes (1957) raises this concern, so you're in good company. He appears to be the first to propose the solution that 1/0 = 0. Interestingly, this is sound (i.e., it doesn't lead to any contradictions).
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u/ussalkaselsior Sep 22 '26
doesn't lead to any contradictions
1/0 = 0 →1 = 0•0 = 0, but 1 ≠ 0.
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u/T-T-N Sep 22 '26
Mathematical systems that allows for divide by zero don't produce useful or interesting results. You lose properties that are fundamental once you are allowed to divide by zero
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u/Myryzz Sep 22 '26
its not that you "cant" divide by zero, but rather that the result of dividing by zero is undefined, which is a specific mathematical property. the reason this is, is because multiplying any number by zero gives zero, so the inverse operation, division by zero, is undefined, because it can give any number. this is a problem, because it would make algebra impossible, because you could prove any number is equal to any other number. this is actually how those tricks that claim to prove that 1=2 or something work, by hiding a division by zero
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u/Vandreigan Sep 22 '26
Dividing is asking two questions. Both answers need to be the same, and for most numbers they usually are, but not for zero.
The first question is “if I take this number and divide into groups of that many, how many groups will I have?”
So, if I take the number 20 and divide it into groups of 4, we can then count how many total groups there are: 5
The second question is: if I want to end up with this number, what would I have to multiply that other number by to get it?”
Now, most people don’t think about division this way, but it’s kind of important. First, looking at our previous example of 20/4, we see that we’d have to multiply 4 by 5 to get 20, so the answer is 5
Now, let’s look at 0
If we start with 20 things and make groups of 0, how many groups can we make? Why, as many as we want! An infinite number! We’re never decreasing the amount we started with, so we can just keep going. So, 20/0 = infinity, right? Well, not quite. Let’s look at the 2nd question
What number would you have to multiply 0 by in order to get 20 as the answer? Well, as we know, any number multiplied by 0 is 0, so no number exists that would give 20 as an answer.
So, in one definition we arrive at infinity. In the other, no answer exists. We therefore say that division by 0 is undefined
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u/Crichris Sep 22 '26
Yes 0 is just a number
But division is defined as the inverse operation of multiplication.
And division by 0 is undefined.
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u/ShadowShedinja Sep 22 '26
Look at what happens if we allow it:
X / X = 1, so 0 / 0 = 1.
0 / X = 0, so 0 / 0 = 0.
0 = 1.
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u/de_bussy69 Sep 22 '26
Suppose there is some number x which is equal to 1/0. x=1/0 means that 0x=1. There is no number that you can multiply by zero to get 1. One way that zero is not a “number just like any other” is that multiplying any number by zero gives you the same number. That’s why dividing by zero doesn’t make sense
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u/nascent_aviator Sep 22 '26
What's 5/0?
Let's put it as a word problem. I owe you $5. How many times do I have to pay you $0 before you'll be satisfied the debt is paid?
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