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Infinity
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Matlock
science forum beginner


Joined: 19 May 2006
Posts: 13

PostPosted: Tue Jun 13, 2006 8:17 am    Post subject: Infinity Reply with quote

Dear Friends

I Have a problem figuring out this. We Know that 1 /
0 is meaningless isn't it.But why 0/0 is meaningless.For example just
look at this
0/0 = 0 * (1/0)
0/0 = 0 since 0 multiplied by any number is zero.

Thanks in advance
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marc.t.davies@gmail.com
science forum addict


Joined: 31 May 2006
Posts: 52

PostPosted: Tue Jun 13, 2006 8:35 am    Post subject: Re: Infinity Reply with quote

Quote:
But why 0/0 is meaningless.For example just
look at this
0/0 = 0 * (1/0)
0/0 = 0 since 0 multiplied by any number is zero.


Because then n/0 = 0

0 = 0/0 = 0(0^-1)

n / 0 = n(0(0^-1))^-1 = n * 0 / 0 = 0

Anyway, why is multiplication by 0 "stronger" than division by 0?
That's an implicit assumption you've made that is not justified.
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Michael11
science forum Guru Wannabe


Joined: 15 Aug 2005
Posts: 103

PostPosted: Tue Jun 13, 2006 10:08 am    Post subject: Re: Infinity Reply with quote

Matlock schrieb:

Quote:
Dear Friends

I Have a problem figuring out this. We Know that 1 /
0 is meaningless isn't it.But why 0/0 is meaningless.For example just
look at this
0/0 = 0 * (1/0)
0/0 = 0 since 0 multiplied by any number is zero.

Thanks in advance

Hi!

It's right: "0 multiplied by any [real] number is zero", but 1/0 isn't
a number. At least not a real one. And if you consider 1/0 = infinity
(which is no real number) then it won't be 0*infinity = 0. There are
some counterexamples in elementary calculus (cf L'H˘pital's rule).

Bye!
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G.E. Ivey
science forum Guru


Joined: 29 Apr 2005
Posts: 308

PostPosted: Tue Jun 13, 2006 10:59 am    Post subject: Re: Infinity Reply with quote

Quote:
Dear Friends

I Have a problem figuring out
roblem figuring out this. We Know that 1 /
0 is meaningless isn't it.But why 0/0 is
meaningless.For example just
look at this
0/0 = 0 * (1/0)
0/0 = 0 since 0 multiplied by any
number is zero.

Thanks in advance

But you just SAID that 1/0 is meaningless! That makes

0*(1/0) meaningless as well. "0 multiplied by any
number is 0", yes, but 0*(1/0) is NOT multiplying "any
number" by 0.

It is true that mathematicians often refer to 1/0 as
"undefined" and 0/0 as "undetermined". The reason for
the difference is this: Saying that a/b= x is exactly the same as saying a= b*x.

If we say 1/0= x for some number x, then we must be saying 1= 0*x- and as you said, "0 multiplied by any number is 0", not 1- there is no such number x.

On the other hand, saying that 0/0= x for some number x, is the same as saying 0= 0*x and that's TRUE- no matter what x is. Rather than saying there is no such number we are saying that x could be anything.

That becomes important in calculating limits: If I am seeking the limit (as x goes to some number a) of a fraction f(x)/g(x), where f and g are continuous at a, the first thing I would do is set x= a. If neither f(a) nor g(a) is 0, then I know the limit is f(a)/g(a). If f(a) is non-zero but g(a) is is 0 (so that f(a)/g(a)= f(a)/0) then I know there is NO
limit. If both f(a) and g(a) are 0 (so that f(a)/g(a)= 0/0) then there MAY be a limit and that limit could be any number.
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Igor
science forum Guru


Joined: 15 May 2005
Posts: 315

PostPosted: Tue Jun 13, 2006 5:15 pm    Post subject: Re: Infinity Reply with quote

Matlock wrote:
Quote:
Dear Friends

I Have a problem figuring out this. We Know that 1 /
0 is meaningless isn't it.But why 0/0 is meaningless.For example just
look at this
0/0 = 0 * (1/0)
0/0 = 0 since 0 multiplied by any number is zero.

Thanks in advance

There's a big difference between 1/0 and 0/0. The former is called
undefined, and the latter is called indeterminant. There is no hope
for the undefined, while there might be for the indeterminant case.
Look up L'Hopital's rule.
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Google

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