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Math derails

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Longfellow Fractally long Since: Apr, 2009
Fractally long
#1: Oct 22nd 2010 at 6:06:49 PM

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.

It Just Bugs Me
DYRE Since: Apr, 2010
#2: Oct 22nd 2010 at 6:40:41 PM

Both of those questions have simple, obvious answers and there's no point arguing them. I'm not sure why people do.

Longfellow Fractally long Since: Apr, 2009
Fractally long
#3: Oct 22nd 2010 at 6:41:57 PM

In my experience, there's always one person who denies 0.999... repeating equals 1.

It Just Bugs Me
Tzetze DUMB from a converted church in Venice, Italy Since: Jan, 2001
DUMB
#4: Oct 22nd 2010 at 6:42:42 PM

Yeah, 1/0 is so obviously zero. limx→0 (sin (x))/(x) = 0, after all!

[1] This facsimile operated in part by synAC.
DYRE Since: Apr, 2010
#5: Oct 22nd 2010 at 6:49:32 PM

^^ Yeah. I know. I'm just wondering why these people are so unwilling to accept one of the numerous proofs that .999...=1 or that x/0 does not equal ∞. It's not hard to confirm that any of these proofs are valid.

edited 22nd Oct '10 6:49:59 PM by DYRE

Madrugada Since: Jan, 2001
#6: Oct 22nd 2010 at 6:54:00 PM

x/0 isn't infinity. It's undefined.

Tzetze DUMB from a converted church in Venice, Italy Since: Jan, 2001
DUMB
#7: Oct 22nd 2010 at 6:54:41 PM

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.
DYRE Since: Apr, 2010
#8: Oct 22nd 2010 at 6:55:36 PM

^^ 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

Ponicalica from facing Buttercup Since: May, 2010
#9: Oct 22nd 2010 at 6:59:19 PM

limx→0 (sin (x))/(x) = 0, after all!
...but that limit is 1 ;_;

the future we had hoped for
Tzetze DUMB from a converted church in Venice, Italy Since: Jan, 2001
Chubert highly secure from California Since: Jan, 2010
highly secure
#11: Oct 22nd 2010 at 7:02:20 PM

^^^ 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

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MrAHR Ahr river from ಠ_ಠ Since: Oct, 2010 Relationship Status: A cockroach, nothing can kill it.
Ahr river
#12: Oct 22nd 2010 at 7:17:40 PM

I IS LEARNING CALCULUS I IS UNDERSTAND.

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Deboss I see the Awesomeness. from Awesomeville Texas Since: Aug, 2009
I see the Awesomeness.
#13: Oct 22nd 2010 at 9:50:58 PM

x/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.
LeighSabio Mate Griffon To Mare from Love party! Since: Jan, 2001
Mate Griffon To Mare
#14: Oct 22nd 2010 at 10:03:57 PM

^ You forgot the pothole.

"All pain is a punishment, and every punishment is inflicted for love as much as for justice." — Joseph De Maistre.
Deboss I see the Awesomeness. from Awesomeville Texas Since: Aug, 2009
I see the Awesomeness.
#15: Oct 22nd 2010 at 10:46:41 PM

...That's the actual justification.

Fight smart, not fair.
Marioguy128 Geomancer from various galaxies Since: Jan, 2010
Geomancer
#16: Oct 22nd 2010 at 11:01:38 PM

...I find it scary that you people are talking about math problems I'm learning in class right now.

You got some dirt on you. Here's some more!
MiyuHimegami Since: Dec, 1969
#17: Oct 22nd 2010 at 11:05:55 PM

More like it's 1/0 that approaches +- infinity if you want a cheap constant.

x/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
This is correct.

edited 22nd Oct '10 11:07:23 PM by MiyuHimegami

Ponicalica from facing Buttercup Since: May, 2010
#18: Oct 23rd 2010 at 12:16:49 AM

There are several ways to construct a real line or complex plane plus infinity.

the future we had hoped for
MiyuHimegami Since: Dec, 1969
#19: Oct 23rd 2010 at 12:17:31 AM

As many as the ways to sample a sinusoid.

spasticgecko Dat Troper from Maryland Since: Oct, 2011
Dat Troper
#20: Oct 23rd 2010 at 1:48:10 PM

So is 0/0 1 or undefined?

Marioguy128 Geomancer from various galaxies Since: Jan, 2010
Geomancer
#21: Oct 23rd 2010 at 1:51:36 PM

Undefined.

You got some dirt on you. Here's some more!
Nyktos (srahc 84) eltit Since: Jan, 2001
(srahc 84) eltit
#22: Oct 23rd 2010 at 1:52:21 PM

"0 divided by 0" literally means "the number that, when multiplied by 0, gives 0" which is...slightly ambiguous.

I guess it is.
Enlong Court Dragon from The Underground Facility Since: May, 2011 Relationship Status: is commanded to— WANK!
Court Dragon
#23: Oct 23rd 2010 at 10:03:58 PM

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...
Uchuujinsan Since: Oct, 2009
#24: Oct 24th 2010 at 2:37:01 AM

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/
MiyuHimegami Since: Dec, 1969
#25: Oct 24th 2010 at 2:46:59 AM

That's the basic proof of why division by zero in a purely algebraic sense is undefined. A decent college algebra textbook should have this proof almost word for word the way the previous poster put it, by the way.


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