# Maths people help!!!

Ok, I have this problem to solve from a friend of mine…
see if you can work it out.

have fun…
I need something to go on the other side of the equals…mike? klaas? help?

Well, I thought you couldn’t do it, but if for some strange reason, you can divide by 0, then wouldn’t the answer be 1? (anything^0 = 1)

I still think you can’t do it.

Andrew

If you evaluate it lazily it becomes a^0 * b^0, or 1.

Phil

Anything^0 is equal to 1, but something divided by zero is not even anything. It is meaningless.

To help my kids with division sums I used to give examples with apples and girls. 2 apples divided between 4 girls is half an apple each. Now zero apples divided between zero girls, how many apples does each girl get? Huh? Which girl? It is meaningless as there are no girls.

Klaas Bil

Edit: this thread should be in J.C.

Re: Maths people help!!!

On Tue, 27 May 2003, phil wrote:

> If you evaluate it lazily it becomes a^0 * b^0, or 1.

Haha! That’s what I was going to say.

Lazy evaluation is your friend :o)

(note to anyone reading on the forum… that’s a smiley with a big nose
above, not an embarrased face - the forum gets it wrong, and I’m not
changing it. Harumph)

Cheers,

Stu

Re: Re: Maths people help!!!

I find lazy evaluation is definitey not my friend, as its presence usually means I’m having to use Haskell or some other horrid, horrid language like that. My brain hurts…

Phil

Re: Re: Re: Maths people help!!!

Offtopic I know, but I have to bite.

[QUOTE]
Originally posted by phil
[B]
I find lazy evaluation is definitey not my friend, as its presence usually means I’m having to use Haskell or some other horrid, horrid language like that. My brain hurts…

Phil [/B][/QUOTE

Horrid? Haskell is one of the most elegant languages around. Not very practical admittedly, but rather beautiful with it.

0 divided by 0 is undefined. but anything to the power of 0 is 1 so im guessing the answer is 1 or undefined. I’ll ask my teach tomorrow and get back to you.

-Budd-

(0/0)^0 * (0/0)^0 =
((0^0)/(0^0)) * ((0^0)/(0^0)) =
(1/1) * (1/1) = 1.

Strictly, 0/0 can be any number (think (0a)/(0b)), but then, any number raised to the power 0 is 1, so I think this is right

Yeah, I thought anything to the power of 0 was 1, so it would be 1

0/0 is undefined. As soon as you divide by zero everything is garbage. you can’t raise an undefined quantity to a power and start getting numbers again, even if you think you know something special about it. For example, anything divided by zero is infinity. We know this because if you take (limit y -> 0) of x/y you get infinity. if you take (limit x->0) you get zero (if y is not zero). So something multiplied by zero is zero. Limit (x->0) of y^x = 0. But then what is (limit x->0) undefined^x? I have no idea. And neither do you. The answer is undefined.
-gauss

But in this case it doesn’t matter whether we have an idea or not, we can work the whole thing out before we need to know what 0/0 actually is.

Phil

Re: Maths people help!!!

On Fri, 30 May 2003, phil wrote:

> gauss wrote:
> > I have no idea. And neither do you. The answer is undefined.
>
> But in this case it doesn’t matter whether we have an idea or not, we
> can work the whole thing out before we need to know what 0/0 actually
> is.

Not quite true. In your lazy evaluation, you’re saying
“anything to the power of 0 is 1”, when in fact you
should be saying “any real (or complex for that matter)
number to the power of 0 is 1”.

If you’re not using lazy evaluation, you can’t assume
that the left half is defined.

What is sheep^0? Is it 1? No, it’s something odd we
haven’t defined yet.

So how can you have undefined^0?

What is undefined+1? We don’t know. It’s undefined.

Cheers,

Stu

if you take a limit on the whole thing using the denominator of the 0/0 bits you get 1

lim ( (0/x)^0 )*( (0/x)^0 ) = 1
(x->0)

You could take lim x->0 x/x which would give 1 also.

Dunno if that makes it the right answer though.

Joe

Sounds like a familiar problem.

Daniel

joe,
you could take the limit of x/(x^2) as x approaches 0. That is 0/0. but the limit is undefined. we don’t have x/x but rather identically 0 divided by identically 0… which is undefined. This isn’t my opinion. It just is. You can’t do math to things that are undefined. If you could, they wouldn’t be undefined… or it wouldn’t be math that you are doing.
-gauss

Just another mathematician adding his 2 cents worth in…

As Gauss and a few others have point out the answer is undefined. Division by zero is meaningless. If you allow division by zero you can do some very wierd things like proving that 1 = 2.

I used to have a lovely proof of this lying around in my head but my brain seems to have forgotten it.

0x1 = 0 = 0x2
Divide by 0.
1 = 2.

The point I was trying to make was that you could expand it so that you weren’t dividing by 0. (0^0 = 1).

I asked my math teacher how to do it and me told me NO! He refused to tell me the answer. I asked him if it was 1 or undefined, but he did not answer. I’ll learn the zero rules next year in math but im stuck right now.

-Budd-

Right, lots of mathematicians have had their say, I’m gonna be all awkward and go for the engineers perspectve (I think. Engineering student at least. Similar outlook, just higher blood alcohol level). The answer is impossible to work out because of the question being purely theoretical (I assume, correct me if I’m wrong) Wether 0 / 0 can be defined is irrelevant, because the whole basis of the question itself is just designed to be awkward.
If the equation is from a real situation, then it must be an approximation, or based on idea behaviour or something like that which means that it doesn’t always work (eg when all variables are 0). If, as I presume, the question is made up by someone trying to be awkward, then the question has about as much meaning as 3 x The fish.

John

Quote of the day: Maths is science without meaning, science is engineering without application.