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Bukkarooo
Posted on 12-29-08 05:04 PM Link | Quote | ID: 97797


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So, I've been doing a ton of thinking about dividing by zero (been bored, ok?). It's always undefined, or just saying "you can't do that". And yet, dividing is seeing how many times one number goes into another number.

With that in mind, let's look at this:

1/0

This is asking how many times 0 goes into 1. Wouldn't it technically go in an infinite amount of times? As 0 has no actual value, it can go an infinite amount of times into any number. Or, we can just have the answer be zero.

I guess my actual question is, wouldn't the answer to any /0 problem just be infinity or 0?

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Kawa
Posted on 12-29-08 05:06 PM Link | Quote | ID: 97798


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I understand it depends on your field. In computer science, the answer is Not A Number and/or raises errors so that's a "you can't do that". In other fields like advanced mathematics, it would be infinity.

Ah yes, Wikipedia agrees.

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boingboingsplat
Posted on 12-29-08 05:08 PM Link | Quote | ID: 97799


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Going with what you said, dividing by zero can be any number between 0 and infinity. So, it's undefined.

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Kawa
Posted on 12-29-08 05:09 PM Link | Quote | ID: 97800


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As good a conclusion as any I'd guess.

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Xeruss
Posted on 12-29-08 07:27 PM Link | Quote | ID: 97804


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You can it you believe in 'Nullity'.


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RT-55J
Posted on 12-29-08 10:49 PM Link | Quote | ID: 97808

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Fortunately, I regained said points after reading the relevant Wikipedia article.

blackhole89
Posted on 12-30-08 12:20 AM Link | Quote | ID: 97812


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Posted by boingboingsplat
Going with what you said, dividing by zero can be any number between 0 and infinity. So, it's undefined.

I can't see how any definition of division would allow a number divided by zero to be, say, 5 without contradictions.

In the real numbers we work with every day, division by zero actually -is- left undefined as a sacrifice towards a cleaner and more consistent definition of various operations, unlike many people who want to boast with their knowledge of "advanced mathematical concepts" assume (and I'd consider myself guilty of it... back in my elementary school days ) - however, there are some approaches to introducing it, each still yielding a whole new set of undefined expressions.


As for that BBC article...
"Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in big trouble. If your heart pacemaker divides by zero, you're dead."

I stopped reading around that point.

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Trax
Posted on 12-30-08 03:21 AM Link | Quote | ID: 97815


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Last view: 2880 days 		My opinion on that matter is that the idea of dividing by zero makes the operation not a division anymore, so I would say the answer cannot possibly be infinity. If you divide by zero, you don't really divide. For example, you have, say, a pie in front of you. You have to divide by zero so you do... nothing. This way there is no answer because no operation was made...

RT-55J
Posted on 12-30-08 04:40 AM Link | Quote | ID: 97823

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Posted by Trax
For example, you have, say, a pie in front of you. You have to divide by zero so you do... nothing. This way there is no answer because no operation was made...

Let's take that same pie and divide it by one. To divide it by one, you do nothing. However, even though "no operation" was made there was an answer. Ergo, you have no idea what you are talking about.

Trax
Posted on 12-30-08 05:21 AM Link | Quote | ID: 97826


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Last view: 2880 days 		Ergo, calmos, it's just rambling on a theoretical problem...
When you divide by one, you take the entire pie with you, and you eat it...
There is an operation...

Dammit, RT-55J, we were comfortable and you throw vinegar in the pot again...

Komaru
Posted on 12-30-08 05:42 AM Link | Quote | ID: 97828


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Wait a second. Dividing is the same as multiplying by the reriprocal of the denominator, right? So the denom. of 5/0 is 0; recip. is 0/1.
Resulting in 5/0=5*(0/1)
But 0/1 is 0,
so 5/0=5*(0)=0

Am I doing something wrong here?

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RT-55J
Posted on 12-30-08 05:53 AM (rev. 2 of 12-30-08 08:47 PM) Link | Quote | ID: 97831

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Last view: 56 days 		@ Komaru: That's merely a proof by contradiction.

EDIT: Wait. What the heck?

Posted by Trax
When you divide by one, you take the entire pie with you, and you eat it...
There is an operation...

Eating the pie would effectively be equivalent to dividing it by infinity (or rather, an absurdly huge number).

Also, here's some food for thought: how exactly would you divide a pie by .5?

Komaru
Posted on 12-30-08 05:56 AM (rev. 2 of 12-30-08 05:57 AM) Link | Quote | ID: 97832


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Posted by RT-55J
@ Komaru: That's merely a proof by contradiction.

Also, here's some food for thought: how exactly would you divide a pie by .5?


Ahh. I completely forgot learning about those. XD

And, dividing by .5 is the same as divding by 1/2, being the same as multiplying by 2.

Also, congrats on post #888!

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Bukkarooo
Posted on 12-30-08 07:02 AM Link | Quote | ID: 97838


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As said earlier, it makes sense that it depends on the field.

And boing: it could -technically- be any number between 0 and infinity. Though in division, you take the largest possible number of times the denominator can go into the numerator. So, it would be infinity.

Not sure how well a physical example works for this... why would you have to divide by 0 to cut a pie? xD But more seriously, you can't really have a physical representation of infinity (unless you count the sideways 8). This is pretty much theoretical. Hell, infinity is just a word we use for all numbers that are larger than 0. It's more a set of numbers. For lack of the infinity symbol, I'm going to put oo.

oo is an element of the set of real numbers (forget the algebraic way of writing that :-P)
oo>0

Because, in division, we take the largest number, if we divide by zero, zero can go in any number of times. once, twice, 57 times, 5k times, 1,345 times, etc. It can go in 983423407*10^100000000000000000000000000000000000000000000 times. In all of those examples, zero can go into the number, it just doesn't change it, as zero is nothing. There is no cap on numbers, so following that zero can go into a number without changing it as many times as you want, there is no cap on that, either. The answer would have to be infinity.

Or, if you're using a computer, it would be undefined, as calculators and such like that try to get an exact, numerical answer. I think is would make sense if calculators started listing problems with division by zero as infinity. My calculator right here (iPod Touch) has the infinity symbol (forgot how I got it the one time I did), but when given a division by zero, it just has error. It would be beneficial, in my opinion, to have calculators list that answer as the infinity symbol.... but then again, I'm not sure how many people would have to do division by zero hehe

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blackhole89
Posted on 12-30-08 09:33 AM Link | Quote | ID: 97841


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Posted by Komaru
Wait a second. Dividing is the same as multiplying by the reriprocal of the denominator, right? So the denom. of 5/0 is 0; recip. is 0/1.
Resulting in 5/0=5*(0/1)
But 0/1 is 0,
so 5/0=5*(0)=0

Am I doing something wrong here?
You are aware that the reciprocal is 1/x, not x/1, right? x/1 is just x again.

Posted by RT-55J
@ Komaru: That's merely a proof by contradiction.
Please, stop making little children cry.

And by that, I mean the little children who, unlike you, actually know maths.

Posted by Bukkarooo
Hell, infinity is just a word we use for all numbers that are larger than 0.
what

Posted by Bukkarooo
It's more a set of numbers.
what

Posted by Bukkarooo
oo is an element of the set of real numbers
It isn't.

Posted by Bukkarooo
Because, in division, we take the largest number, if we divide by zero, zero can go in any number of times. once, twice, 57 times, 5k times, 1,345 times, etc. It can go in 983423407*10^100000000000000000000000000000000000000000000 times. In all of those examples, zero can go into the number, it just doesn't change it, as zero is nothing. There is no cap on numbers, so following that zero can go into a number without changing it as many times as youwant, there is no cap on that, either. The answer would have to be infinity.
No, and infinite times zero still is zero. You are implying that has some nonzero value... or, even worse, as it would be a direct consequence of your assumption, all nonzero values.

Why is it that people are so keen in discussing things they don't even make a serious effort to get a basic understanding of?

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Ailure
Posted on 12-30-08 09:57 AM Link | Quote | ID: 97842

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Posted by Bukkarooo
Hell, infinity is just a word we use for all numbers that are larger than 0.
In other words, ∞ = 42 or some other random number chosen by a fair dice roll! Defiantly makes math problems so much easier!!

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Kawa
Posted on 12-30-08 09:59 AM Link | Quote | ID: 97843


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Posted by Ailure
In other words, ∞ = 42 or some other random number chosen by a fair dice roll! Defiantly makes math problems so much easier!!
That'd be four.

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James Freeman
Posted on 12-30-08 06:30 PM Link | Quote | ID: 97862


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Posted by Bukkarooo
Hell, infinity is just a word we use for all numbers that are larger than 0.

I am currently resisting the urge to punch your face in.

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RT-55J
Posted on 12-30-08 09:00 PM Link | Quote | ID: 97870

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Posted by blackhole89
Please, stop making little children cry.

And by that, I mean the little children who, unlike you, actually know maths.

I overestimated his intelligence and somehow missed the fact that he was trying to prove that multiplication and division by zero were equivalent. Forgive me, master.

Posted by blackhole89
No, and infinite times zero still is zero.

I thought that it was undefined. Or does that depend on the branch of mathematics?

MathOnNapkins
Posted on 12-30-08 10:35 PM Link | Quote | ID: 97873


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when we speak of "infinite times zero is still zero" we mean limits of sequences and such times zero will still approach zero. Infinity is not the kind of number you can just toss around and multiply and add with. It's not a member of the real numbers. There is the definition of the "extended real numbers" which basically is the normal Reals and throws in positive and negative infinity on either end. But this definition is only used to make certain range expressions nicer.

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