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        riddles >> what happened >> Infinity=???
        
(Message started by: mikedagr8 on May 15th, 2008, 4:40am)
Title: Infinity=???
Post by mikedagr8 on May 15th, 2008, 4:40am
I was playing around with my calculator the other day and I found a unique problem.

I used infinity(http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/infty.gif) in an equation and I ended up with a non-zero, non-one, non error answer.  What did I type in?

There may be many answeres, but this one is on the keypad for most graphics calculators.
Title: Re: Infinity=???
Post by Grimbal on May 15th, 2008, 5:26am
tanh?
Title: Re: Infinity=???
Post by mikedagr8 on May 15th, 2008, 5:30am
Um, that's not what I typed in, so I can't say if that is correct. I can say that you aren't far off.:-X

Is tanh=tan(http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/i.gif)?
Title: Re: Infinity=???
Post by gotit on May 15th, 2008, 6:03am
What Grimbal meant was that you typed tan-1(infinity) which gives pi/2.
Title: Re: Infinity=???
Post by mikedagr8 on May 15th, 2008, 6:05am
Oh, then yes.
Title: Re: Infinity=???
Post by ThudanBlunder on May 15th, 2008, 6:27am

on 05/15/08 at 06:03:53, gotit wrote:
What Grimbal meant was that you typed tan-1(infinity) which gives pi/2.

No, tanh is short for 'hyperbolic tangent', which also does the trick.
Title: Re: Infinity=???
Post by gotit on May 15th, 2008, 7:08am

on 05/15/08 at 06:27:08, ThudanBlunder wrote:
No, tanh is short for 'hyperbolic tangent', which also does the trick.


Yup. I know that. :)
Title: Re: Infinity=???
Post by cheesepuff on May 15th, 2008, 7:56am
You mean something like arctan?
Title: Re: Infinity=???
Post by Sir Col on May 15th, 2008, 9:49am
2^(1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/infty.gif)*r, where r is any real number you want the final value to be.
Title: Re: Infinity=???
Post by Grimbal on May 16th, 2008, 9:57am
There also is the 2-key sequence [C], [1].
Title: Re: Infinity=???
Post by Sir Col on May 16th, 2008, 11:33am
Nice idea, Grimbal. Although it has to be "non-one", so I guess [C], [2] would do.
Title: Re: Infinity=???
Post by Grimbal on May 16th, 2008, 2:09pm
Hey!?!  The problem was changed?  I am sure there was no mention of "no-one".
OK, no one, then.


on 05/15/08 at 05:30:12, mikedagr8 wrote:
Is tanh=tan(http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/i.gif)?



on 05/15/08 at 07:56:15, cheesepuff wrote:
You mean something like arctan?


It was the hyperbolic tangent, defined as
tanh(x) = (exp(x)-exp(-x))/(exp(x)+exp(-x))
tanh(+infinity) = 1

But well, that was before the problem was amended.
Title: Re: Infinity=???
Post by mikedagr8 on May 19th, 2008, 12:58am

on 05/16/08 at 14:09:58, Grimbal wrote:
Hey!?!  The problem was changed?  I am sure there was no mention of "no-one".
OK, no one, then.



It was the hyperbolic tangent, defined as
tanh(x) = (exp(x)-exp(-x))/(exp(x)+exp(-x))
tanh(+infinity) = 1

But well, that was before the problem was amended.

The only thing which was changed was the infinity symbol which didn't appear originally. Everything else was left the same. As I said, tan-1(http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/infty.gif) was what I typed in.
Title: Re: Infinity=???
Post by Grimbal on May 19th, 2008, 1:01am
Sorry, then I don't know how to read.  :'(
Title: Re: Infinity=???
Post by mikedagr8 on May 19th, 2008, 4:51am

on 05/19/08 at 01:01:21, Grimbal wrote:
Sorry, then I don't know how to read.  :'(

No need to apologise, especially to me, if anything; I owe you the apology for not saying anything earlier.
Title: Re: Infinity=???
Post by iono on May 19th, 2008, 7:40pm
Can't you just do infinity over 2xinfinity, or is there something wrong with that?
Title: Re: Infinity=???
Post by Sir Col on May 20th, 2008, 8:45am
I'm afraid infinity over infinity is indeterminate.

Consider L = (kx+1)/x, where k is any finite value. If x "equals" infinity then k*infinity = infinity, infinity+1 = infinity, so L = infinity/infinity, and we might think the answer is 1. However...

From L = (kx+1)/x we divide top and bottom by x to get L = (k+1/x)/1 = k+1/x. Now as x tends towards infinity we can see that L approaches k.

In other words, we can make "infinity/infinity" equal to any arbitrary value we should choose.
Title: Re: Infinity=???
Post by iono on May 20th, 2008, 7:43pm
All I got were the first and last sentences
Title: Re: Infinity=???
Post by Sir Col on May 20th, 2008, 11:46pm
Let's take an example and work through it slowly...

Suppose L = (2x + 1) / x.

If we make x "equal" infinity then 2x = infinity, 2x + 1 = infinity, so L = infinity / infinity.

But if we simplify the expression by dividing (2x + 1) by x, we get 2x/x + 1/x = 2 + 1/x.
Now if we make x "equal" infinity then 1/infinity = 0, so L = 2.

In other words, we have shown that L = infinity / infinity = 2.

But we could do the same again with L = (3x + 1) / x, and show that infinity / infinity = 3, and so on.
Title: Re: Infinity=???
Post by ima1trkpny on May 21st, 2008, 4:00pm

on 05/20/08 at 23:46:48, Sir Col wrote:
...
In other words, we have shown that L = infinity / infinity = 2.

But we could do the same again with L = (3x + 1) / x, and show that infinity / infinity = 3, and so on...

Hmmm maybe someone should show this to srn347, I mean temporary... *cough cough*
Title: Re: Infinity=???
Post by iono on May 21st, 2008, 5:28pm
Ok, I think I get it. but whats wrong with x/2x where x=infinity?

and why doesn't  ALT code work in BB?
Title: Re: Infinity=???
Post by Eigenray on May 21st, 2008, 9:13pm
The expression A/B is defined only if there is a unique C such that A = B*C.

For example, 1/0 and 1/infinity are undefined because there is no C such that 1 = 0*C, or 1 = infinity*C.  On the other hand, 0/0 and infinity/infinity are undefined because there are infinitely many C such that 0 = 0*C, or infinity = infinity*C.
Title: Re: Infinity=???
Post by iono on May 22nd, 2008, 5:11pm
Ahh. I see.


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