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Acmlm's Board - I3 Archive - General Chat - Zero division?! New poll | |
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Omega45889

Shyguy


 





Since: 11-18-05

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Posted on 12-16-05 02:16 AM Link | Quote
Welcome to calculus 1...
NSNick

Gohma
IF ALL ELSE
FAILS USE FIRE
BOOZE








Since: 11-17-05
From:

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Posted on 12-16-05 02:17 AM Link | Quote
Originally posted by Squash Monster
Originally posted by NSNick
lim   1  =  Infinity
x->0  x



The end.

Nope, not quite. I had that answer at the end of my post and had to edit it because I made the same mistake.

The limit of that is infinity if you approach from the positive, or negative infinity if you approach from the negative.

So there's no actual value for the normal limit.

Which really does a lot to explain why things end up breaking when people try to assign values to 1 / 0.



Fixed.
Alastor
Fearless Moderator Hero








Since: 11-17-05
From: An apartment by DigiPen, Redmond, Washington

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Posted on 12-16-05 02:40 AM Link | Quote
Am I the only one not seeing a difference here?

What was fixed?
Jagori

150


 





Since: 11-17-05

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Posted on 12-16-05 04:06 AM Link | Quote
x->0 became x->0+ (approaching 0 from the positive side)
HyperHacker

Star Mario
Finally being paid to code in VB! If only I still enjoyed that. <_<
Wii #7182 6487 4198 1828


 





Since: 11-18-05
From: Canada, w00t!
My computer's specs, if anyone gives a damn.
STOP TRUNCATING THIS >8^(

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Posted on 12-16-05 10:25 AM Link | Quote
I see no +.
MathOnNapkins

1100

In SPC700 HELL


 





Since: 11-18-05

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Posted on 12-16-05 11:11 AM Link | Quote
If you view it in the complex plane, all infinities are the same, so you don't need a + or -. It's just a complex number with arbitrarily large modulus (radius).

It's nice to muse about what 1/0 is, but it's important that you keep in mind that you will have to make a new "algebraic" structure to put it in. The only reason you can't divide by zero in your typical number systems (they're called Rings and Fields) is that they simply were not designed with it in mind. You can't divide by zero in fields b/c by definition whoops the axioms 0 * a = 0, where a is any number in the field. Therefore you can't find any number such that 0 * a = 1, unless 0 = 1, in which case your ring MUST be the trival ring with one element {0}.

I had a thread in Lost Threads on the old board where I developed a system of how to work with 1/0 and powers of 1/0. That doesn't mean it's the only system. Small hacker's definition is built upon a logical deduction based on how you usually expect to handle numbers, but it will break your ring structure if you use it.

edit again: btw, does anybody know why the Lost Threads are still restricted on the archive, whereas the staff forums aren't?

(edited by MathOnNapkins on 12-16-05 10:12 AM)
(edited by MathOnNapkins on 12-16-05 10:12 AM)
(edited by MathOnNapkins on 12-16-05 10:16 AM)
spel werdz rite









Since: 11-19-05

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Posted on 12-16-05 04:41 PM Link | Quote
Lets look at this:
1/1=1
1/0.5=2
1/0.25=4
1/0.125=8
You guys are assuming that the smaller the denominator gets, the larger the number will be.
Lets say you go low enough to 1/0.0000000001=1,000,000,000
You're saying that after it decreases more (now we'll say zero), it would be that largest number possible, even infinite.
1/0=Infinity
But what happens if it were to still decrease? Will it get even higher?
1/-0.0000000001=-1,000,000,000
1/-0.125=-8
1/-0.25=-4
1/-0.5=-2
1/-1=-1
1/0 doesn't work because it's the cross between extremely large and extremely small.
Here's another example:
1/10=0.1
1/100=0.01
1/1,000=0.001
1/10,000=0.0001
This time, the larger the denominator, the smaller the number. If it were one divided by an extremely large number (infinity) it would be zero.
But look at its oppposite.
1/-10=-0.1
1/-100=-0.01
1/-1,000=-0.001
1/-10,000=-0.0001
The smaller the denominator, the larger the number. If this time it were one over an extremely small number (-infinity) it would once again be zero.
Look at the graph y=1/x. The asymptopes of the graph display were the function does not work. If anyone has a basic Algebra II education, they would know this. We've had professional mathematicians for the last 5,000 years, we know what were talking about.
Crystal Shards
Newcomer


 





Since: 12-14-05
From: St. Catharines

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Posted on 12-16-05 05:01 PM Link | Quote
Wow. You guys are getting WAY too into this.

The premise behind his equation (though not necessarily the ones expressed by the users here), lies in this statement:

"In other words, Z is a "number", so unlogically big that when it's multiplied by 0, it becomes 1."

I stopped reading after that, as there was no point. Regardless of how illogically big the number is- it could encompass twice the space of the universe with it's hugeness- if you have zero quanity of that number, then you have nothing, typically expressed by the word zero. Anything whatsoever x 0 = 0. Always.
MathOnNapkins

1100

In SPC700 HELL


 





Since: 11-18-05

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Posted on 12-16-05 05:11 PM Link | Quote
Wow, Shards is back. How long were you away? Are you still homeless?
spel werdz rite









Since: 11-19-05

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Posted on 12-16-05 05:16 PM Link | Quote
Originally posted by Crystal Shards
Wow. You guys are getting WAY too into this.
Obsessions are what allow things to be great.
Crystal Shards
Newcomer


 





Since: 12-14-05
From: St. Catharines

Last post: 6720 days
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Posted on 12-16-05 05:17 PM Link | Quote
Way too long, and no, I've got a steady job, and an appartment. Thanks though.
jordan_mega_gamer

Red Goomba


 





Since: 11-25-05
From: Vermont, USA

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Posted on 12-16-05 09:23 PM Link | Quote
Okay, this is getting far too complex for a 10th grader like myself, but I'll try to contribute anyway. You really don't need the math for this situation, because it's kind of common sense.

Let me take the classic cookie example. Say you're dividing a cookie amongst people. How much of a cookie will each person get? What happens if we divide a cookie amongst 0 people? The common sense answer is, "Who cares?" The whole point of division is to divide something into X equal parts. If you're dividing by 0, you're pretty much saying, "Okay, we have one cookie divided into 0 pieces. How big is each piece?" It doesn't work, but it doesn't need to work.

On the other hand, let's say you're dividing a cookie into an infinite number of pieces. How big is each piece? Well, usless you plan of splitting an atom, and thus destroying the cookie entirely, there'll always be a little left. You can't cut something into such tiny pieces that it vanishes. Again, it doesn't work, but doesn't really need to. I agree with Squash Monster: it's best viewed as a limit.

Of course, maybe something like this is somewhat useful in more advanced math. This is from a 10th-grader's point of view. And IMO, there just can't be multiple infinities. The definition of infinity is the biggest possible number. Thus, if there's a bigger infinity, it'd become the new and only infinity.
spel werdz rite









Since: 11-19-05

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Posted on 12-17-05 03:36 AM Link | Quote
Originally posted by Mari0mega
Okay, this is getting far too complex for a 10th grader like myself.
I'm in 10th grade, and I discussed this with math teachers when I was in eighth grade.
Zem
Permabanned. Flaming, trolling, reregistering.


 





Since: 11-18-05

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Posted on 12-17-05 04:35 AM Link | Quote
Originally posted by spel werdz rite
Originally posted by Mari0mega
Okay, this is getting far too complex for a 10th grader like myself.
I'm in 10th grade, and I discussed this with math teachers when I was in eighth grade.

What do you want, a prize?
spel werdz rite









Since: 11-19-05

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Posted on 12-18-05 03:23 AM Link | Quote
Originally posted by Zem
Originally posted by spel werdz rite
Originally posted by Mari0mega
Okay, this is getting far too complex for a 10th grader like myself.
I'm in 10th grade, and I discussed this with math teachers when I was in eighth grade.

What do you want, a prize?
A block of gold will do.
Make it 1/0 pounds.
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