You can't divide zero by zero. Zero divided by zero isn't one.

Any number divided by zero is undefined.

Oh yeah??? Says who? ;-)

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"Yeah, no one likes a smartass, but we all like stars" - Thom Yorke


smartasscoach.tri-oeiras.com

I was always under the impression that zero divided by anything is always 0. Can't come up with a quantity of something that never existed.

?

Anything but zero divided by zero is zero.

Try putting zero divided by zero in Excel or Microsoft's calculator. Doesn't come up with a number.

Let's use an example:

You have one person with zero cycling ability.

Put that person OVER a bike with PC's (zero effect)

0/0

You don't get a cyclist (ONE). The real answer is undefined... :-D

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"Yeah, no one likes a smartass, but we all like stars" - Thom Yorke


smartasscoach.tri-oeiras.com

I got confused I guess. Any number to the zero power is one. Doesn't that include Zero?

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Frank,
An original Ironman and the Inventor of PowerCranks

I was taught that "division by zero is impossible." I know my spreadsheets won't let me do it.

But so much of history is being re-written based on what I see in kids textbooks. I guess maybe that's true with math, too.

I better stop before this gets booted to the lavender room.

Bob C.

"Doesn't that include zero?"

Short answer: No

Longer answer from a web site (I can't follow it too far....)

Zero to the Zero Power

It is commonly taught that any number to the zero power is 1, and zero to any power is 0. But if that is the case, what is zero to the zero power?

Well, it is undefined (since xy as a function of 2 variables is not continuous at the origin).

But if it could be defined, what "should" it be? 0 or 1?

Presentation Suggestions:
Take a poll to see what people think before you show them any of the reasons below.

The Math Behind the Fact:
We'll give several arguments to show that the answer "should" be 1.

* The alternating sum of binomial coefficients from the n-th row of Pascal's triangle is what you obtain by expanding (1-1)n using the binomial theorem, i.e., 0n. But the alternating sum of the entries of every row except the top row is 0, since 0k=0 for all k greater than 1. But the top row of Pascal's triangle contains a single 1, so its alternating sum is 1, which supports the notion that (1-1)0=00 if it were defined, should be 1.
* The limit of xx as x tends to zero (from the right) is 1. In other words, if we want the xx function to be right continuous at 0, we should define it to be 1.
* The expression mn is the product of m with itself n times. Thus m0, the "empty product", should be 1 (no matter what m is).
* Another way to view the expression mn is as the number of ways to map an n-element set to an m-element set. For instance, there are 9 ways to map a 2-element set to a 3-element set. There are NO ways to map a 2-element set to the empty set (hence 02=0). However, there is exactly one way to map the empty set to itself: use the identity map! Hence 00=1.
* Here's an aesthetic reason. A power series is often compactly expressed as
SUMn=0 to INFINITY an (x-c)n.
We desire this expression to evaluate to a0 when x=c, but the n=0 term in the above expression is problematic at x=c. This can be fixed by separating the a0 term (not as nice) or by defining 00=1.

I just blew a really big snot bubble.

Nerd...! ;-)

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"Yeah, no one likes a smartass, but we all like stars" - Thom Yorke


smartasscoach.tri-oeiras.com

Well sure, doesn't evryone know that?

[reply]Anything but zero divided by zero is zero.[/reply]

Exactly - nothing divided by nothing has to be nothing (or actually it is "undefined" because of what nothing is).

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Life isn't measured by the number of breaths we take, but by the number of moments that take your breath away.

I used to be good in math...my mind has gone to mush. I'm dreading when my now 5-year-old starts having homework that requires me to relearn everything! At least now there are math help internet sites out there....

actually, 0 divided by 0 is any real number you want...

proposition (quite trivial): if a is a real number, then there exists 2 functions f and g on some real var. x that tends to 0 when x tends + infinity, such that

lim f(x)/g(x) = a when x tends to infinity

et voila!

By that logic, then nothing divided by nothing could be infinity. You could also fit an infinite amount of nothing into nothing. That is why it is undefined.

Oh dear God, this is why I ASK the math questions instead of trying to answer them. But doesn't my logic follow, just a little? If you have nothing and try to divide it by nothing, you have something that is undefinable.....

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Life isn't measured by the number of breaths we take, but by the number of moments that take your breath away.

[reply]
By that logic, then nothing divided by nothing could be infinity. You could also fit an infinite amount of nothing into nothing. That is why it is undefined.[/reply]

But an infinite amount of nothing is still nothing. Therefore the "infinite" part doesn't really matter.

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Life isn't measured by the number of breaths we take, but by the number of moments that take your breath away.

no...you are right...the non smartass answer is that it is undefined

bien!

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Life isn't measured by the number of breaths we take, but by the number of moments that take your breath away.

Unless of course it is part of a differentiable equation. And in this case we can take the limit, the engine will stop running after the car has stopped. Therefore, the gas mileage is zero ;-)



Or we get into Les Hospitals method.



P.S. I still want that bioinformatics info of some sort. Even a couple of your or your cohorts papers.

Daniel

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The question of who is right and who is wrong has seemed to me always too small to be worth a moment's thought, while the question of what is right and what is wrong has seemed all-important.

-Albert J. Nock

What you guys are missing is that zero is simply a placeholder and has no value and is therefore not actualy a number, but an abstraction of a lack of a number. Your answer, as many have said is undefined.

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Dave Stark
dreamcatcher@astound.net
USAC & USAT level 2 certified coach

[reply]
Or we get into Les Hospitals method.
[/reply]

I can't believe this thread got so far before anyone mentioned L'Hopital's Rule.

Francois stated the rule, but didn't name drop for a compatriot! The man's name is Guillaume Francois Antoine de l'Hoptial.

A more compact solution of the indeterminate form 0/0 can be stated:

Consider B as any real number (meaning not imaginary as in not involving the square root of a negative number)

also consider f(x) and g(x) being two functions (like f(x)=x+2 and g(x)=x-1)

if lim(x->B) f(x)=0 and lim(x->B) g(x)=0
then lim(x->B) [f'(x)/g'(x)]=L
where L is a real number and f'(x) and g'(x) are the derivatives of f(x) and g(x) with respect to x.

Wow. What a strange thread this became. The things I miss when I'm grocery shopping.

Frank, I think your confusion is stemming from trying to apply "ordinary" mathematics (i.e. mathematics that most people encounter in everyday life) to an extraordinary situation (the (mathematically) interesting question of when infinity pops up).

As you have seen in the responses to this thread, there are many interpretations to the answer of "what is 0/0". This is precisely the reason that mathematicians say it is undefined.

L'H^opital's rule doesn't really apply here, because you are asking about the specific value of 0/0, not the limiting behavior of a pair of functions.


It's also interesting that the thread evolved into a discussion of the different question "what is zero raised to the zeroth power?". Seems to be a completely different question, but whatever. Basically, mathematicians have defined 0 raised to the zeroth power to be 1. This is really just to make things easier on ourselves. The reason is that it's quite simple to show that the limit of a^x as x approaches zero is equal to 1 for any a not equal to zero. So by defining 0^0 to be 1 as well, we clean up a lot of potential mess.

There are many reasons why I love mathematics. Teaching it, and trying to make people understand how interesting it can be, is at the very top of the list.

-Colin

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Any run that doesn't include pooping in someone's front yard is a win.