Yeah, 1/0 is so obviously zero. limx→0 (sin (x))/(x) = 0, after all!
[1] This facsimile operated in part by synAC.I don't believe in the continuum hypothesis. Whatchagonnadoaboutit, punk??
^He said "does not equal".
edited 22nd Oct '10 6:55:01 PM by Tzetze
[1] This facsimile operated in part by synAC.^^ Indeed. People who say it's infinity clearly aren't even bothering to think. Like, why would it be positive infinity and not negative infinity? You have an equally strong case that it would be either, by the logic of people who say it is infinity, anyway. And a million other reasons why it doesn't make sense.
edited 22nd Oct '10 6:56:21 PM by DYRE
^^^ I think, from the viewpoint of a precalc person, that it's good to know that it doesn't really equal zero, but nice to remember that so you're good with your vertical asymptotes.
edited 22nd Oct '10 7:02:32 PM by Chubert
Whatcha gonna do, little buckaroo? | i be pimpin' madoka ficsx/0 is the same as infinity on a graph due to the fact that it is a regular sized number of an incredibly small number, which results in the number exploding to infinity.
Fight smart, not fair.^ You forgot the pothole.
"All pain is a punishment, and every punishment is inflicted for love as much as for justice." — Joseph De Maistre.More like it's 1/0 that approaches +- infinity if you want a cheap constant.
edited 22nd Oct '10 11:07:23 PM by MiyuHimegami
There are several ways to construct a real line or complex plane plus infinity.
the future we had hoped for"0 divided by 0" literally means "the number that, when multiplied by 0, gives 0" which is...slightly ambiguous.
I guess it is.Ah, so it's undefined because it could literally be any number, from negative ∞ to positive ∞.
Which explains why it tends to be represented on a graph as the graph curving down to negative infinity on one side of the number, and up to positive infinity on the other side.
I have a message from another time...The common definition of fields does not explicitly define division or substraction. Substraction is "addition with the inverse", while division is "multiplication with the inverse". So a-b is a+(-b), where -b is such that b+(-b) = 0 (neutral element of addition) and a/b is a*(b^(-1)) with b^(-1) such that b*b^(-1)=1 (neutral element of multiplication. Let's say there exist a q such that 0 * q = 1 meaning x/0 would be defined as x*q, so q would be the inverse of 0. Then would follow 1 = q*0 = q*(0*0) = (q*0)*0 = 1*0 = 0. As an obvious result that would mean all numbers are equal. So unless you want all numbers to be equal (or sacrifice other, very basic axioms I used for the proof - well technically, 0*0 = 0 is not an axiom, you can proof it as a homework), a division by zero has to be undefined.
Btw, lim (x->0) (0/x) = 0, so saying the result is something like infinity is often wrong. That's why it is undefined, and it's good that way.
Pour y voir clair, il suffit souvent de changer la direction de son regard www.xkcd.com/386/

You can be in the heat of the flamiest war or the deepest discussion; just throw out "hey guys, is 0.999 repeating equal to 1?" or "x/0 is infinity" and everybody's inner pedant will feel compelled to call a truce and butt in. It's beautiful.
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