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Topic: Infinity=??? (Read 1419 times) |
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mikedagr8
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Infinity=???
« on: May 15th, 2008, 4:40am » |
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I was playing around with my calculator the other day and I found a unique problem.
I used infinity( ) 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.
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| « Last Edit: May 15th, 2008, 5:30am by mikedagr8 » |
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Grimbal
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Re: Infinity=???
« Reply #1 on: May 15th, 2008, 5:26am » |
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tanh?
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mikedagr8
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Re: Infinity=???
« Reply #2 on: May 15th, 2008, 5:30am » |
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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.
Is tanh=tan( )?
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| « Last Edit: May 15th, 2008, 5:32am by mikedagr8 » |
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gotit
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Re: Infinity=???
« Reply #3 on: May 15th, 2008, 6:03am » |
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What Grimbal meant was that you typed tan-1(infinity) which gives pi/2.
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mikedagr8
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Re: Infinity=???
« Reply #4 on: May 15th, 2008, 6:05am » |
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Oh, then yes.
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ThudnBlunder
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Re: Infinity=???
« Reply #5 on: May 15th, 2008, 6:27am » |
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on May 15th, 2008, 6:03am, gotit wrote:| What Grimbal meant was that you typed tan-1(infinity) which gives pi/2. |
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No, tanh is short for 'hyperbolic tangent', which also does the trick.
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gotit
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Re: Infinity=???
« Reply #6 on: May 15th, 2008, 7:08am » |
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on May 15th, 2008, 6:27am, ThudanBlunder wrote:
No, tanh is short for 'hyperbolic tangent', which also does the trick.
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Yup. I know that. 
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cheesepuff
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Re: Infinity=???
« Reply #7 on: May 15th, 2008, 7:56am » |
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You mean something like arctan?
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Sir Col
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Re: Infinity=???
« Reply #8 on: May 15th, 2008, 9:49am » |
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2^(1/)*r, where r is any real number you want the final value to be.
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Grimbal
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Re: Infinity=???
« Reply #9 on: May 16th, 2008, 9:57am » |
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There also is the 2-key sequence [C], [1].
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Sir Col
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Re: Infinity=???
« Reply #10 on: May 16th, 2008, 11:33am » |
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Nice idea, Grimbal. Although it has to be "non-one", so I guess [C], [2] would do.
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Grimbal
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Re: Infinity=???
« Reply #11 on: May 16th, 2008, 2:09pm » |
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Hey!?! The problem was changed? I am sure there was no mention of "no-one".
OK, no one, then.
on May 15th, 2008, 5:30am, mikedagr8 wrote:| Is tanh=tan()? |
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on May 15th, 2008, 7:56am, cheesepuff wrote:| You mean something like arctan? |
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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.
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mikedagr8
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Re: Infinity=???
« Reply #12 on: May 19th, 2008, 12:58am » |
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on May 16th, 2008, 2:09pm, 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. |
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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() was what I typed in.
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| « Last Edit: May 19th, 2008, 12:58am by mikedagr8 » |
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Grimbal
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Re: Infinity=???
« Reply #13 on: May 19th, 2008, 1:01am » |
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Sorry, then I don't know how to read. 
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mikedagr8
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Re: Infinity=???
« Reply #14 on: May 19th, 2008, 4:51am » |
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on May 19th, 2008, 1:01am, Grimbal wrote:Sorry, then I don't know how to read.
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No need to apologise, especially to me, if anything; I owe you the apology for not saying anything earlier.
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iono
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Re: Infinity=???
« Reply #15 on: May 19th, 2008, 7:40pm » |
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Can't you just do infinity over 2xinfinity, or is there something wrong with that?
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Sir Col
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Re: Infinity=???
« Reply #16 on: May 20th, 2008, 8:45am » |
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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.
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iono
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Re: Infinity=???
« Reply #17 on: May 20th, 2008, 7:43pm » |
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All I got were the first and last sentences
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So, if I help you, I'll get kicked for ksing, but if I don't, then I'll get kick for not helping...
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Sir Col
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Re: Infinity=???
« Reply #18 on: May 20th, 2008, 11:46pm » |
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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.
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ima1trkpny
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Re: Infinity=???
« Reply #19 on: May 21st, 2008, 4:00pm » |
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on May 20th, 2008, 11:46pm, 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... |
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Hmmm maybe someone should show this to srn347, I mean temporary... *cough cough*
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iono
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Re: Infinity=???
« Reply #20 on: May 21st, 2008, 5:28pm » |
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Ok, I think I get it. but whats wrong with x/2x where x=infinity?
and why doesn't ALT code work in BB?
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| « Last Edit: May 21st, 2008, 5:30pm by iono » |
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So, if I help you, I'll get kicked for ksing, but if I don't, then I'll get kick for not helping...
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Eigenray
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Re: Infinity=???
« Reply #21 on: May 21st, 2008, 9:13pm » |
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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.
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iono
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Re: Infinity=???
« Reply #22 on: May 22nd, 2008, 5:11pm » |
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Ahh. I see.
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So, if I help you, I'll get kicked for ksing, but if I don't, then I'll get kick for not helping...
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