Divide by Zero?

[ShawnLee]

http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml


This guy says he's created a new method to dividing by zero. Create a new number and call it nullity. He's teaching this method.

How does this solve anything? Call me non-creative, but isn't this just the same thing as saying that we don't divide by zero? "Call it nullity and leave it at that" vs. "Don't do it and leave it at that" seems the same to me.

[Grafalgar]

Well, it's really not that different from using an "imaginary number": √(-1) = i

This "nullity" could be used to make certain math problems much simpler / possible.

[Thesifer]

Why isn't it just "If you divide by 0 you get 0" or even "If you divide by 0 you get the same number" Like... 23 Divided out 0 times is 23. Or 23 Divided by 0 is 0. Wouldn't it be easy enough to come up with a rule and stick to it?
Isn't most math made up anyways? Or am I wrong about that?

[cadetevon]

He tried to make this "nullity" applicable to pacemakers, airplane autopilots and car computers...

Last I checked those machines only do the math and computing that we humans make them do. So, my fix is that we don't have these things compute x/0 and be done with it.

Unless, of course, I'm being rather daft and don't realize it.

In concept, though, this is intriguing.

[Markel]

Well, it's really not that different from using an "imaginary number": √(-1) = i
Except that i comes into some pretty interesting mathematical relationships, such as Euler's formula: e^(i*pi) = -1

To me, it sounds like this guy is just trying to create another term for infinity, since that is the limit as the denominator approaches 0.

[Napoleon54]

Why isn't it just "If you divide by 0 you get 0" or even "If you divide by 0 you get the same number" Like... 23 Divided out 0 times is 23.

Since 23/1 = 23, then you'd be forced to say that 0=1, which is obvioulsy not true. So that one doesn't work.


Or 23 Divided by 0 is 0.

That one seems logical to me. Since 23*0 = 0, and division is the converse of multiplication, it seems logical that 23/0 = 0. But who knows, there's gotta be some reason mathematicians haven't agreed to that in the past.


Wouldn't it be easy enough to come up with a rule and stick to it? Isn't most math made up anyways? Or am I wrong about that?

HEHE, it is made up IMO. I've argued that point with my mathematician friends just to get them riled up. It's all in good fun, nobody gets truly angry or upset. Another interesting debate is wether math is a science. They say 'yes' and I say 'no'. They seem to think that labelling math as a branch of science would give it some status or validity. I say it's just a bunch of abstract junk. The POV that I take in those debates is that math isn't useful until it is applied to real life problems, at which point it becomes science or engineering and isn't strictly math anymore. Don't get me wrong though, I really do admire mathematicians, and what they do is useful WHEN IT IS APPLIED TO SOLVE A PROBLEM. Experimental math is a worthy pursuit because eventually a lot of it is put to use to solve real problems, but until that happens it really is useless. For some reason "useless" carries a negative connotation, even though it is an accurate word to use. Perhaps I should try a euphamism (i.e. something that means the exact same thing but sounds more PC), like unapplied, it has unrealized potential, etc... :shrug: :P

[Markel]

That one seems logical to me. Since 23*0 = 0, and division is the converse of multiplication, it seems logical that 23/0 = 0. But who knows, there's gotta be some reason mathematicians haven't agreed to that in the past.
Ever try to go from just below infinity to zero in an infinitely small interval? The shock is just too much to take. :P

[ShawnLee]

Higher maths deal with this stuff, and yeah, it does progressively approach infinity. I didn't figure this out conceptually until AFTER calculus, unfortunately, but that's why my calculators kept making REALLY high mountain peaks semi-randomly.

With everyone saying, why not zero divided by zero, or making x over zero being defined as one or zero, it's because zero has special properties. I read a good page yesterday when I first posted this that asked, when are apples equal to oranges? When you have zero of them. That a non-value exists is huge, and I don't see how this guy just creates an imaginary number that means nothing? It seems almost... sacriligious to me.

[Markel]

That one seems logical to me. Since 23*0 = 0, and division is the converse of multiplication, it seems logical that 23/0 = 0.
Just to address the above:

23*0 = 0 We're good here. Let's divide both sides by 23:
0 = 0/23 Still good. You want to say that
23/0 = 0. So lets multiply both sides by 0 and get:
23 = 0*0. But if we allow division by 0, we could divide both sides of the original equation by 0 and get:
23 = 0/0 But the same would apply to 22, 21, and every other value, which would "prove" that 1=2=3=4=5=6.... = big problem....

Once you try to allow division by 0, mathematics falls apart.

[Napoleon54]

Just to address the above:

23*0 = 0 We're good here. Let's divide both sides by 23:
0 = 0/23 Still good. You want to say that
23/0 = 0. So lets multiply both sides by 0 and get:
23 = 0*0. But if we allow division by 0, we could divide both sides of the original equation by 0 and get:
23 = 0/0 But the same would apply to 22, 21, and every other value, which would "prove" that 1=2=3=4=5=6.... = big problem....

Once you try to allow division by 0, mathematics falls apart.

cool :thumbup:

[Kevster]

I had a mathematics professor in college who seriously threatened to call your parents if you ever attempted to write a proof containing '1/0' anywhere. '1/0' is indeterminate and simply calling it something other than that does not prove it is true. Graf's suggestion about the substitution of 'i' for √(-1) as being the same thing is incorrect. We still have to deal with √(-1), we just give it a symbol to handle it easier. It is an 'imaginary' concept that becomes very important in electrical engineering, particularly in power engineering. In that example you have to deal with 'real' power and 'reactive' power (where √(-1) is used to simplfy the equation) and if you do not account for it, things go to hell in a handbasket real quick (as in stuff explodes).

Now a few things to ponder: why he is ruining these children's education instead of trying to teach this to university level students? Because they might question his faulty logic? Because he doesn't have the balls to publish his 'findings' and have real mathemeticians rip it to shreds in their critiques?

[ShawnLee]

Now a few things to ponder: why he is ruining these children's education instead of trying to teach this to university level students? Because they might question his faulty logic? Because he doesn't have the balls to publish his 'findings' and have real mathemeticians rip it to shreds in their critiques?
That's what I was wondering. It's an interesting question of what he's trying to accomplish here.

[zippyjuan]

You could take a number, divide it by one, and call it a wholity.

[InfiniteNothing]

Higher maths deal with this stuff, and yeah, it does progressively approach infinity.
From left to right (like we read) it approaches -infinity

[Burzhui]

Why isn't it just "If you divide by 0 you get 0" or even "If you divide by 0 you get the same number" Like... 23 Divided out 0 times is 23. Or 23 Divided by 0 is 0. Wouldn't it be easy enough to come up with a rule and stick to it?
Isn't most math made up anyways? Or am I wrong about that?


because 23/1 = 23 and thus 23/0 can not be 23 because 1 != 0

[Houdini]

Yeah, it is undefined, or infinity, which as someone once said "I can only contemplate the infinite for a finite time," whichever way you want to see it.

4/2=2
4/1=1
4/(1/2) = 8
4/ (1/4) = 16
4/ (1/8) = 32
4/smaller you go = bigger you get, so
4/0 = high as you can go, therefore undefined, unless you want to coin a stupid term for it. :shrug:

[Kevster]

because 23/1 = 23 and thus 23/0 can not be 23 because 1 != 0

To follow up on what you're saying for Thesifer's comment, using calculus you can approximate what the function 1/x will do as x approaches zero using a limit function. For the limit function f(y)=1/x as x approaches 0, f(y) will approach infinity. You cannot simply have x=0, as the function will blow up.

[Burzhui]

To follow up on what you're saying for Thesifer's comment, using calculus you can approximate what the function 1/x will do as x approaches zero using a limit function. For the limit function f(y)=1/x as x approaches 0, f(y) will approach infinity. You cannot simply have x=0, as the function will blow up.
yup

[zenbooty]

unless you want to coin a stupid term for it. :shrug:
Divide overflow.

[Houdini]

Divide overflow.

Perfect!

[InfiniteNothing]

Yeah, it is undefined, or infinity, which as someone once said "I can only contemplate the infinite for a finite time," whichever way you want to see it.

4/2=2
4/1=1
4/(1/2) = 8
4/ (1/4) = 16
4/ (1/8) = 32
4/smaller you go = bigger you get, so
4/0 = high as you can go, therefore undefined, unless you want to coin a stupid term for it. :shrug:
It only approaches infinity from the right. From the left it gets smaller and smaller.
4/-2=-2
4/-1=-1
4/(-1/2) = -8
4/ (-1/4) = -16
4/ (-1/8) = -32

But yeah, 1/x definitely doesn't approach 0.

[Markel]

It only approaches infinity from the right. From the left it gets smaller and smaller.
4/-2=-2
4/-1=-1
4/(-1/2) = -8
4/ (-1/4) = -16
4/ (-1/8) = -32
More correctly, it becomes increasingly more negative. I believe that negative infinity still qualifies as infinity.

[InfiniteNothing]

Yeah it depends on what system of math you're in. Since we're on the internet I'm going to have to cite IEEE floating-point standard and say that -infinity and +infinity are distinct values with distinct binary values.

Now who wants to figure out what 1/0 * 0 is?

[Markel]

YSince we're on the internet I'm going to have to cite IEEE floating-point standard and say that -infinity and +infinity are distinct values with distinct binary values.

How many bits of precision are you using to store infinity? :P

[VTGreg]

Yeah it depends on what system of math you're in. Since we're on the internet I'm going to have to cite IEEE floating-point standard and say that -infinity and +infinity are distinct values with distinct binary values.

Now who wants to figure out what 1/0 * 0 is?

It is indeterminate. 0/0 is indeterminate, thus anything multiplied by that value is indeterminate.

[InfiniteNothing]

Well, yeah, but that's no fun. Lets try and fathom what happens when 0 gets multiplied by positive and negative infinity at the same time.

[ShawnLee]

I'm gonna call nerd-out on this and end discussion. It doesn't work? Oh well. I tried.

[zenbooty]

Well, yeah, but that's no fun. Lets try and fathom what happens when 0 gets multiplied by positive and negative infinity at the same time.
There is no spoon.

[Markel]

Well, yeah, but that's no fun. Lets try and fathom what happens when 0 gets multiplied by positive and negative infinity at the same time.
That starts to remind me of some things that were covered in an upper level Analysis class, where we considered different levels of infinities (aleph-null, C, etc.) - some of the stuff Georg Cantor burdened us with.

[cadetevon]

42!! Where is my towel when I need it?

[GraingerGuy]

Don't Panic.










;)

[VTGreg]

Well, yeah, but that's no fun. Lets try and fathom what happens when 0 gets multiplied by positive and negative infinity at the same time.

Well, zero times anything is zero. Following that logic, it would be zero.

[InfiniteNothing]

That starts to remind me of some things that were covered in an upper level Analysis class, where we considered different levels of infinities (aleph-null, C, etc.) - some of the stuff Georg Cantor burdened us with.
You know you're in trouble when your math class starts using hebrew.

[Markel]

You know you're in trouble when your math class starts using hebrew.
You know you're in trouble when the math problem you are expected to solve involves integrating over an infinite number of discontinuities. (Yes, this really happens.)

[attgig]

(joiningthis conversation late..)

so, let's say x/0 = nullity.


what do you get when you have a formula like:

(23/0)*12+56?

is it... 12nullity+56?
or is it nullity (like infinity would be).
and if it is nullity... once you divide by 0, no other operations are possible... then what benefit do we get out of it?

I like the lim x->0 of 1/x as clearer and more sensible explanation of this problem.

or better yet, maybe we should call verizon and ask them how to solve this.