/sci/ - Science & Math

[Anonymous No.3888604]

Hey /sci/, just wondering, why can't one divide by zero? Is there a proof of why this doesn't work or it simply an axiom?

[Anonymous No.3888613]

Can you split something into zero parts?

[Anonymous No.3888622]

it depends on the kind of math you're doing
if you're asking, presumably, you're doing relatively simple arithmetic (algebra)
basically if you allow it to have an answer you can create paradoxes, nonsensical statments

[Anonymous No.3888629]

>>3888613
I'm looking for a mathematical proof

[Anonymous No.3888634]

>Is there a proof of why this doesn't work or it simply an axiom?
>axiom

by definition actually

[Anonymous No.3888641]

If you have an object A, then an inverse B is an object, such that

A·B=1

Since 0·B=0 (and not =1) by the definition of 0, there can't be an inverse of 0 in the algebraic sense presented here.

[rutrohraggy No.3888650]

>>3888634
This is correct.
0 was one of the greatest inventions/discoveries of math/numbers.

Seriously.

The concept of zero wasn't well understood or accepted for a long long time.

[Anonymous No.3888656]

Axiom, for many reasons.

One, it doesn't make any sense. Say you have 5 cupcakes, and you want to divide it into zero parts. Well, by merely stating that the cupcakes exist, they must be arranged into some type of groups, even if it's merely the 5 together (5/1). Putting it into zero groups implies that they no longer exist, which doesn't make sense.

Also, as mentioned, accepting division by zero allows for paradoxes. For example:
1*0 = 2*0
Dividing by zero yields:
1 = 2
Which is clearly false.

[Anonymous No.3888659]

Because, zero is a human construct, it doesn't actually exist.

Sounds like a cop out, but Zero doesn't exist.

Well, I mean you "Can" divide by zero, all you get is infinity set of numbers.

[Anonymous No.3888723]

>>3888659
No numbers actually exist.
We can have a certian number of things, but then we can have zero of something.
This doesn't mean that these numbers are 'real' (except, fo course, in the mathematical sense)

[Anonymous No.3888768]

"Zero" is usually used to mean the additive identity of a ring (an algebraic structure with addition, subtraction, and multiplication, but not necessarily division, and the operations must satisfy some familiar requirements), and in this context division by 0 IS possible, but it implies that the ring only has one element. This result can be proven, and it is why you generally call division by 0 impossible.

Proof that division by 0 is possible in a ring with only one element:
If there is only one element n, then n + n = n and n*n = n are the only ways to define multiplication and addition. Then n + a = a for all a, so n = 0. Then for all b, there exists a unique a such that a*0 = b, because that equation is always the same as n*n = n. This means that b/0 is always defined, so division by 0 is possible.

Proof that if a ring allows for division by 0, the ring only has one element:
For any a in a given ring, a + 0 = a. Multiplying both sides by a gives a(a + 0) = a*a. Distributivity of multiplication over addition gives a*a + a*0 = a*a (= a*a + 0). Subtracting a*a from both sides gives a*0 = 0. In particular 0*0 = 0
If 0 has a multiplicative inverse, call it 0' (0*0' = 1), then 0*0*0' = 0*0', which yields (0 =) 0*1 = 1. Then for a an arbitrary element of the ring, multiplying both sides of the previous equation by a gives (0 =) a*0 = a*1 (= a), so in fact the only element of this ring is 0.

The upshot is that division by zero isn't really possible unless you're not using a conventional notion of zero (or unless 0 is your only element). Some people say wheel theory allows division by zero, and to be honest I haven't looked that far into it, but it's always looked to me like wheel theory has defined a new operation and simply labeled it as "division by zero" without it actually being directly related.

Hope this makes sense, let me know if theres anything confusing here.

[Anonymous No.3888818]

>>3888604
n = any number
x = any number

0 = 0/X
n/0 = n * (X/0)

keeps on repeating

[Anonymous No.3888872]

>>3888768
Let me edit the first sentence:
I mean in the context of a structure where both an "addition" and a "multiplication" operation exist. 0 in a more general sense is the identity of an abelian group using additive notation, but I'm ignoring that because no multiplication (and therefore no division) is present, so it's not relevant to the question.

[Vortex Ops No.3888898]

It's common sense.

[Anonymous No.3888936]

>>3888613
> Can you split something into zero parts?

Wrong. x/0 means "how many zeroes are in x?". You can't answer that one unless you give a set of answers, like {0,1,2,...,infinity}. There is no one answer, therefore the operation is UNDEFINED.

[Anonymous No.3888952]

>>3888936
Therefore 0 = infinity

[Anonymous No.3888959]

>>3888952
I meant X/0 = infinity

[Anonymous No.3888976]

>>3888959
No, in a mathematical sense the proper term is undefined, it is not infinity as you think of it. It's tempting to think of it that way, but it is wrong.

[Anonymous No.3888986]

>>3888952

No, shitball. A SET OF ANSWERS is not just one answer. There is MORE THAN ONE ANSWER. The operation assumes JUST ONE ANSWER. Get that through your thick motherfucking shitskull.

infinity =/= {0,1,2,...,infinity}

[Anonymous No.3889005]

>>3888986
A set is only one object, so it is one answer.

[Anonymous No.3889114]

>>3889005
You shouldn't talk about set theory when you haven't taken the classes or studied it at all. It makes you look stupid, and nobody enjoys that. I know I sure don't, and I'm pretty sure you don't like looking stupid.

[Anonymous No.3889315]

Well OP using the basic hyperbola (y=x^-1) we can see that when x=0 y is extremely large... or it could be anything at all.
therefore it is undefined
also if you try on your computer's calculator it will tell you it can't be done. Which should be all the incentive you need not to try it

[Anonymous No.3889921]

The only slightly legitimate operation for division by zero is 0/0, which produces (or is valid for) all real numbers.

Anything else is impossible by definition; let me demonstrate simply.

1/0 = x

Moving to one side to isolate the 1;

1 = x*0

There is no possible number x that satisfies this relation; generalizing it for all numbers, i can say that

n = x*0

n immediately, regardless of x, can only be 0; rewriting gives

0 = x*0

which is satisfied by x being equal to any existent real number. Therefore, isolating the x;

0 / 0 = x = all numbers in the real domain.

A layman's explanation, no set theory hullabaloo.