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HungryJoe Gristknife from Under the Tree Since: Dec, 2009
Gristknife
#26: Oct 24th 2010 at 9:03:28 AM

Woah, meta. A thread about Math derails becomes a math derail, with no discussion of the subject at hand.

Charlie Tunoku is a lover and a fighter.
Chubert highly secure from California Since: Jan, 2010
highly secure
#27: Oct 24th 2010 at 10:31:40 AM

@ Enlong: no, that's not true.

0/0 is never an asymptote. Get a grapher, and graph f(x)= (x-3)/(x-3). It will be a straight line. Now check out the "table" function of your grapher- at 3, it should say "undefined" or something like that. something/0 makes asymptotes, 0/0 makes undefined.

Whatcha gonna do, little buckaroo? | i be pimpin' madoka fics
LouieW Loser from Babycowland Since: Aug, 2009
Loser
#28: Oct 24th 2010 at 10:53:52 AM

I dislike math derails because they remind me that I have pretty much no real knowledge in any subject, especially not math.

edited 24th Oct '10 10:54:22 AM by LouieW

"irhgT nm0w tehre might b ea lotof th1nmgs i dont udarstannd, ubt oim ujst goinjg to keepfollowing this pazth i belieove iN !!!!!1 d
Enlong Court Dragon from The Underground Facility Since: May, 2011 Relationship Status: is commanded to— WANK!
Court Dragon
#29: Oct 24th 2010 at 11:14:04 AM

[up][up] I didn't say 0/0.

Sorry if I confused things, but I was thinking [x]/0.

I have a message from another time...
DYRE Since: Apr, 2010
#30: Oct 24th 2010 at 12:08:00 PM

^^ I like them because I don't have a whole lot of math knowledge, but math is fun, so I like reading about it.

Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
Tzetze DUMB from a converted church in Venice, Italy Since: Jan, 2001
Deboss I see the Awesomeness. from Awesomeville Texas Since: Aug, 2009
I see the Awesomeness.
#33: Oct 24th 2010 at 5:34:23 PM

Yeah, 0/0 is technically 1 but it's an instantaneous displacement. Although my math teacher explained it using a rectangle.

edited 24th Oct '10 5:34:54 PM by Deboss

Fight smart, not fair.
Ponicalica from facing Buttercup Since: May, 2010
#34: Oct 24th 2010 at 8:37:15 PM

0/0 only equals one if it's the limit of a ratio that ends up being 1.

L'Hopital's rule is that if f(x) and g(x) both approach 0 as x approaches c, then lim(x→c) f(x)/g(x) = lim(x→c) f'(x)/g'(x).

the future we had hoped for
Deboss I see the Awesomeness. from Awesomeville Texas Since: Aug, 2009
I see the Awesomeness.
#35: Oct 24th 2010 at 9:49:32 PM

We have a rectangle with side lengths a and b. The area of the rectangle is therefore a*b. Now, imagine that b=1/a. So we can now establish that the area of the rectangle is a*1/a or 1. Now substitute 0 or infinity for a. Mind=blown.

Fight smart, not fair.
Ironeye Cutmaster-san from SoCal Since: Jan, 2001 Relationship Status: Falling within your bell curve
Cutmaster-san
#36: Oct 24th 2010 at 9:53:30 PM

Of course, it works just as well for 2/a, pi/a, 3000000/a, and so on.

I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.
Ponicalica from facing Buttercup Since: May, 2010
#37: Oct 24th 2010 at 11:07:36 PM

Deboss: You can't make that substitution in the real numbers though.

the future we had hoped for
Deboss I see the Awesomeness. from Awesomeville Texas Since: Aug, 2009
Ironeye Cutmaster-san from SoCal Since: Jan, 2001 Relationship Status: Falling within your bell curve
Cutmaster-san
#39: Oct 24th 2010 at 11:50:54 PM

When infinity becomes a real number, the mathematical community will be sure to let everyone else know. wink

Edit: More seriously, infinity isn't a real number and can't be plugged in. Additionally, 1/x is undefined at 0, so the rectangle can't have length if you plug in 0. (ie It ceases to be a rectangle)

edited 24th Oct '10 11:53:41 PM by Ironeye

I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.
Uchuujinsan Since: Oct, 2009
#40: Oct 25th 2010 at 2:58:15 AM

You could argue that 0/0 = 0^(-1) * 0 equals 1, as it WOULD be the definition of 0^(-1), that it is such that it equals 1, but as 0^(-1) doesn't exist in any number system that is relevant (afaik there where some bored mathematicians who constructed a number system where this works) it "technically" is undefined :/

Now everyone repeat: "Undefined".

The area of a rectanle A = a*b, if you want to transform it into b=A/a you have to divide by a, which you can do for every a that is not zero (or infinity if you use a system where it is included). So no, you can't substitute a=0 because your prerequisite for your transformation is a != 0.

@Ironeye
There are projective planes who use R unified with +- infinity as an additional element, but it still doesn't solve the problem with division by zero, as allowing it would always have unwanted consequences.

Pour y voir clair, il suffit souvent de changer la direction de son regard www.xkcd.com/386/
KylerThatch literary masochist Since: Jan, 2001
literary masochist
#41: Oct 25th 2010 at 6:18:42 AM

So, 1. Is it equal to 1, or is it a not-actually-a-number-at-all, or what?

And why?

This "faculty lot" you speak of sounds like a place of great power...
MiyuHimegami Since: Dec, 1969
#42: Oct 25th 2010 at 7:14:17 AM

IIRC that's indeterminate.

However, take any integer n >= 1 but less than infinity though, and you can prove that 1n = 1 by mathematical induction.

Let's see, um, take the base x = 1. So 11 = 1.

Assume that this holds for x = z such that 1z = 1.

Prove that it holds for z+1:

1z+1 = 1z * 11.

Since 11 = 1 and 1z = 1 by the hypothesis, then 1z * 1 = 1 by induction.

This does not hold when n = infinity, by the way, since yeah, indeterminate...

edited 25th Oct '10 7:29:51 AM by MiyuHimegami

Ironeye Cutmaster-san from SoCal Since: Jan, 2001 Relationship Status: Falling within your bell curve
Cutmaster-san
#43: Oct 25th 2010 at 7:26:46 AM

@Uchu: Well, yes, I was assuming that we were in Euclidean space and weren't using any extended real number system in place of the standard real line. If one had to use such things, it would push the "proof" out of the realm of the simple and easy to understand.

I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.
Ponicalica from facing Buttercup Since: May, 2010
#44: Oct 25th 2010 at 9:17:22 AM

1 is indeterminate. For example, limx→∞1x=1, but limx→∞(1+1/x)x=e.

edited 25th Oct '10 9:18:47 AM by Ponicalica

the future we had hoped for
Longfellow Fractally long Since: Apr, 2009
Fractally long
#45: Oct 25th 2010 at 9:26:53 AM

I tend to think of these 0/0s and 1^infinities as crossroads in the world of math.

edited 25th Oct '10 9:27:06 AM by Longfellow

It Just Bugs Me
MrCharles Head of Security from ???????? Since: Oct, 2010
Head of Security
#46: Oct 25th 2010 at 9:29:25 AM

Have you guys forgotten where you are? Anything can equal anything.

Do you remember how you got here?
Belian In honor of my 50lb pup from 42 Since: Jan, 2001
In honor of my 50lb pup
#47: Oct 25th 2010 at 12:19:05 PM

My number comments/jokes (that are completely Off Topic):

  • 2+2=fish and 3+3=glasses or 8tongue
  • Why is it dangerous to do math in the jungle? Add four and four and you get ate
  • (completely unrelated to the other comments) Here is a riddle for you: How can you add two single digit numbers together and get a number >18?
  • Make sense of this statement:
  • 11 was a racehorse
  • 22 was 12
  • 1111 race
  • 22112

edited 25th Oct '10 12:20:02 PM by Belian

Yu hav nat sein bod speeling unntil know. (cacke four undersandig tis)the cake is a lie!
KylerThatch literary masochist Since: Jan, 2001
literary masochist
#48: Oct 25th 2010 at 12:24:09 PM

Man. Things get weird at infinity. (Or approaching infinity, if you prefer.)

This "faculty lot" you speak of sounds like a place of great power...
Yej (4 Score & 7 Years Ago) Relationship Status: They can't hide forever. We've got satellites.
HungryJoe Gristknife from Under the Tree Since: Dec, 2009
Gristknife
#50: Oct 25th 2010 at 2:08:50 PM

^^^2 and 0 make 20.

Charlie Tunoku is a lover and a fighter.

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