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Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 04, 2011 - 22:27 Reply with quote Back to top

WhatBall wrote:
I've identified the mathematicians by highlighting their inability to laugh at a silly answer to a math related question. Very Happy
If it was funny we would have laughed Razz
GAZZATROT



Joined: Apr 26, 2009

Post   Posted: Oct 04, 2011 - 22:28 Reply with quote Back to top

By the way Paul I've decided to politely decline that invite to your next night of fun. Wink

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Forever fearless, sometimes stupid.
GAZZATROT



Joined: Apr 26, 2009

Post   Posted: Oct 04, 2011 - 22:35 Reply with quote Back to top

@Sutherland.... you're getting a little tetchy with your responses. I'll just point out that you can't agree with me.... I'm telling you. Very Happy

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Forever fearless, sometimes stupid.
Shraaaag



Joined: Feb 15, 2004

Post   Posted: Oct 04, 2011 - 22:37 Reply with quote Back to top

This reminds me of Zeno's paradoxes:
Pasted from wikipedia (cause I'm too lazy to write it myself):
Quote:
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise

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happygrue



Joined: Oct 15, 2010

Post   Posted: Oct 04, 2011 - 22:41 Reply with quote Back to top

Many words or symbols mean the same thing. Is there any difference between those iconic "no diving" signs (with a diver and a circle with a diagonal line through it to mean no diving) or a sign that says "no diving"? I think this is an argument about symbols rather than about the actual math.

If you want proofs then there are many, but many people aren't swayed by them. Instead I'd like to develop further something that Sutherlands said:

Sutherlands wrote:

First, by the real number theorum, between any two distinct real numbers, there is another number which is the average of the two. What is the average of 1 and .99999...? There is no number between them.


In advanced math the idea of numbers (or other things) being equal to each other is demonstrated by showing that there is no difference between them. If you claim that 1 and 0.9999... are different numbers then there must be some actual difference between them. You could subtract one from the other and get something that is not zero. But try to imagine what that difference is. If you pick any number and claim it's the difference between 1 and 0.9999... then obviously you are wrong because you just "go a few nines farther" and suddenly the claim is clearly not true any more.

I know it hurts the brain - I argued with my math professor the first time he jokingly brought it up, but a little research shows that "math people" agree on this. There is a whole field of study that does proofs using these ideas. Here is some other quick backup to my case:

http://bobobobo.wordpress.com/2008/01/20/how-to-do-epsilon-delta-proofs-1st-year-calculus/

http://en.wikipedia.org/wiki/0.999...


Finally, as an aside to other math geeks - because I can't help but bring it up given the context of this thread - I'll leave you with the common joke:

Let epsilon be less than zero.

(that's it)

EDIT: In the time it took me to write this things have already taken a detour into flamewar territory so I just want to mention that I didn't read the last ten or so posts when writing this...
Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 04, 2011 - 22:46 Reply with quote Back to top

happygrue wrote:
Finally, as an aside to other math geeks - because I can't help but bring it up given the context of this thread - I'll leave you with the common joke:

Let epsilon be less than zero.
Had to look it up to get it Razz
happygrue



Joined: Oct 15, 2010

Post   Posted: Oct 04, 2011 - 22:52 Reply with quote Back to top

Sutherlands wrote:
happygrue wrote:
Finally, as an aside to other math geeks - because I can't help but bring it up given the context of this thread - I'll leave you with the common joke:

Let epsilon be less than zero.
Had to look it up to get it Razz


Yeah, at first you go "huh?" but it gets better and better as time goes by. Very Happy
Vesikannu



Joined: Mar 06, 2011

Post   Posted: Oct 04, 2011 - 22:55 Reply with quote Back to top

I see someone has been reading Cracked (item #4).

In before eleven page long flamewar.
DukeTyrion



Joined: Feb 18, 2004

Post   Posted: Oct 04, 2011 - 22:56 Reply with quote Back to top

Sutherlands wrote:
DukeTyrion wrote:
The problem is, the decimal system can never quite be exact.
Give me a fraction that can't be represented as a decimal, please.


Pi
Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 04, 2011 - 22:58 Reply with quote Back to top

DukeTyrion wrote:
Sutherlands wrote:
DukeTyrion wrote:
The problem is, the decimal system can never quite be exact.
Give me a fraction that can't be represented as a decimal, please.


Pi
Seriously? You think Pi is a fraction?
James_Probert



Joined: Nov 25, 2007

Post   Posted: Oct 04, 2011 - 22:59 Reply with quote Back to top

DukeTyrion wrote:
Sutherlands wrote:
DukeTyrion wrote:
The problem is, the decimal system can never quite be exact.
Give me a fraction that can't be represented as a decimal, please.


Pi

unfortunately, can't be represented as a fraction, either.

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Brad



Joined: May 16, 2005

Post   Posted: Oct 04, 2011 - 22:59 Reply with quote Back to top

There is a vital difference between .999... and 1 when dealing with limits and calculus, especially as you approach critical points. Unfortunately it just gets more confusing as you start using this maths to answer such questions as 'from what direction do we approach infinity?', and sometimes 1 exactly can't be evaluated, where as .999... (or even 2 - .999...) are critically important values.

For those with too much time on their hands, dig out your old graphics calculator and try plugging in y=(-1/(x+1))+1 or y=(sin(x-1))/(x-1) - you'll see that no value is possible for 1, but as you close in on it from either side vast changes occur to the graph. For those who still have too much time - wiki "Maths" & "Limits", and see how far down the page you can get.

(I'll crawl back into my geek corner now to watch the latest Big Bang Theory)

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quixote



Joined: Mar 13, 2005

Post   Posted: Oct 04, 2011 - 23:00 Reply with quote Back to top

Yeah, Sutherlands was being a little loose with his terminology there. He should have asked for a rational number that can't be represented as a decimal.

As someone that has studied a fair bit of mathematics, 0.9999... is equal to 1 in all the ways that matter. Clearly they're not identical in every respect (they *look* different) but saying that there are not equal misses the point. They are equal in the same way that "five", "5", "V", "4.999...", "10/2" etc. are all different representations of the same idea.
DukeTyrion



Joined: Feb 18, 2004

Post   Posted: Oct 04, 2011 - 23:04 Reply with quote Back to top

Sutherlands wrote:
DukeTyrion wrote:
Sutherlands wrote:
DukeTyrion wrote:
The problem is, the decimal system can never quite be exact.
Give me a fraction that can't be represented as a decimal, please.


Pi
Seriously? You think Pi is a fraction?


It might be an irrational number, but it's a hell of a lot easier to just represent it at 355/113 Wink
DukeTyrion



Joined: Feb 18, 2004

Post   Posted: Oct 04, 2011 - 23:06 Reply with quote Back to top

quixote wrote:
They are equal in the same way that "five", "5", "V", "4.999...", "10/2" etc. are all different representations of the same idea.


Except 'V' was about space lizards eating humans
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