What is zero divided by zero anyways? I tried researching it and got a slew of answers, I hope someone can solve this for me.
I believe the answer would be the same as any other number divided by 0 - undefined.
Consider: 6/0 == you have six items and you put 0 in each box. How many boxes do you use?
Likewise: 0/0 == you have zero items and put zero in each box. How many boxes do you use?
Zev Steinhardt
It isn’t anything. As z noted, it is undefined. There is no answer, because no answer exists.
For more info and explanation, Google on *“division by zero” undefined .
Let’s try this again:
It isn’t anything. As zev noted, it is undefined. There is no answer, because no answer exists.
For more info and explanation, Google on “division by zero” undefined .
While 0/0 would certainly be undefined, what about
lim [sub]a → 0[/sub] a/a
Wouldn’t the answer be 1?
But doesn’t nothing go into nothing 1 time?
3 * x/4 * x
Normally x can equal any number since the x’s cancel out right? So why is this any different from 0?
yep, and
lim[sub]a->0[/sub] 0/a = 0 and lim[sub]a->0[/sub] 2a/a = 2
Generally, when you say “X divided by Y gives Z”, you mean that Z is the unique number such that Z times Y is X.
So, if “0 divided by 0 gives Z”, then z must be the unique number such that Z times 0 is 0.
However, Z times 0 = 0 is true for all numbers (integers, fractions, real numbers, complex – it doesn’t matter).
Therefore there is no unique number Z, and 0 divided by 0 has to be meaningless.
Dvsion is usually defined as:
a/b = a*b[sup]-1[/sup]
where b[sup]-1[/sup] is the multiplicative inverse of b. An mathematical object containing an additive identity (0) and a muplicative inverse (for all a !+ 0) is called a field (the real numbers are a field); a field cannot contain a muplicative inverse, so divison by zero is undefined.
That should be for all a != 0.
Wikipedia on Division by zero.
This is the explanation I have seen, with the term for 0/0 being “indeterminate” as opposed to “undefined.”
Argh! the last line should be: " a filed cannot contain a multiplicative inverse for zero".
This implicitly is assuming a notion of limit. 0 exists in any field independant of a topological structure sufficient to consider the limits some posters are suggesting.
0/0 is undefined because 0 is by definition noninvertible in any ring.
Yes 0/0 is undefined. But no one said why. 0/0 is undefined because if it were defined to be any number, then you can literally prove that any number is equal to any other number. And we can’t let that happen, can we?
So it appies to rings in general? I’m guessing that’s because a*0 = 0 in any ring.
It’s undefined because divison by zero cannot be defined in a ring full-stop.
“My brain hurts”
ZipperJJ (mathless journalism student and former Algebra II dropout)
Well, actually I may have to back up from what I said before. Under some circumstances it is beneficial to allow the trivial ring with one element. Note that most axiom systems for rings explicitly disallow that one because it’s often annoying, but doesn’t violate the other axioms.
That is, in the unique field with one element, 0/0 = 0, where 0 acts as both additive and multiplicative identity.
For a concise but insightful explanation, I recommend this proof sketch by Preston et al.