pi
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Pi is irrational, like my ex-wife. Fortunately, neither is infinite. Both go on forever, without end, for no good reason, never repeating any sensible pattern. Thank God that Pi can't hold a credit card. "...a photo album is like Life, but flat and stuck to pages." - Shog9
Wow - that was TRULY a great line! :laugh: _:laugh: __:laugh: ___:laugh: ____:laugh:
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Nathan A. wrote:
as if I said that I'm thinking of a number between 1 and infinity, and you were to guess, that you have "almost no" chance of guessing correctly
On the opposite I would argue you probably thought of 42 or some other integer number in the vicinity :-D However I have some friend having a Math PhD and they tend to think to number such exp(log(pi+1))... ;P No, seriously, you're right!
Nathan A. wrote:
So, "almost all" real numbers are transcendental.
Well, yeah... But truth to tell, real human being don't use them ;P
Nathan A. wrote:
Was that kid sister safe?
:laugh: Well, sort of :-D
Super Lloyd wrote:
On the opposite I would argue you probably thought of 42 or some other integer number in the vicinity
Yeah, the idea of picking a random number from the set of Natural numbers is kind of weird, and defenitly not something humans or computers can do(I doubt it's possible to do). So for instance, if we played that game, and I picked a number, for any natural number, there is probability 1 that my number is greater than yours. There's a game a group of people can play, where everyone has 20 seconds to write down the largest number they can think of. So you can write things like "1,000,000" and "100^100^100^100" and "1000!" and "the millionth prime" and anything you can write down. So if you extend the game so that when people are born they are immediatly taught arithmetic and conscripted into writing numbers for the rest of their lives (imagine a cruel, mathematical version of the matrix), you can think of the biggest think a person could write. Since anyone can only write a finite number of charecters in their lifetime, there is a limit to what can be written down by a single human, so there is a limit on what can cumulatively be written by mankind over the history of the universe. Therefore, out of the finite # of things that can be written down by humanity, there are a finite # of those which correspond to large integers and so there is a largest. You can find a similar number for computers the same way. Therefore, any number larger than that is completely outside the realm of our comprehension in any shape or form forever. So if we play the guessing game, even from 1 to infinity, you really have a nonzero probability of guessing my number, since I can really only pick from a finite number. This is in opposition to really picking a number at random from 1 to infinity, because, if you did pick a natural number at random, with probability 1 it will be greater than the "largest number accessible by minds of men or machines". But the funny thing is: while as a mathematician I can no longer say there is "almost no" chance of you guessing my number(because the probability no longer equals 0), as a reasonable human being, thinking about the set of numbers humans and computers can theoretically "think of", I'm more certain than ever you have almost no chance of matching two random numbers from that set!
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Vikram A Punathambekar wrote:
I thought that was implicit
Well, not implicit, this comes from : a = x^2 a - x^2 = 0 (a-x)(a+x) = 0 solutions are x=a AND x=-a. ~RaGE();
Hey, I know that. :-D I meant something like "Yes, I know we say SQRT(49) is 7, but implicitly -7 is equally valid too; it's just that we don't say it every time". Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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Pi is irrational, like my ex-wife. Fortunately, neither is infinite. Both go on forever, without end, for no good reason, never repeating any sensible pattern. Thank God that Pi can't hold a credit card. "...a photo album is like Life, but flat and stuck to pages." - Shog9
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
Here's my take... it's not infinite. It just can't be described in finite terms with the constraints of a base-10 number system. Also - it's not a number, really....it's a relationship between two other values. Now...you've got to ask...why can't we measure those things precisely? Because not everything in the universe is made to fit in a base-10 number system. The universe wasn't built on base 10... humans just try to measure it in that range because that's how many fingers we have....? I'd bet that in another system of measurement, things like pi and the golden ratio come out even... Tim Shay
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
The term "irrational number" is not an explanation; the term is a definition. XYZ smart guy said, "My oh my, look at that number! Ain't it peculiar? I think I will call that kind of peculiarity "irrational."" Thus, XYZ, the first geek (probably), wasn't trying to understand why. He was just naming a peculiarity of the number that makes it different from another kind, like an "integer." If you want to know "why," you have to go back to pi as the relationship of two parts of a circle. And, I'm not even sure that gives you a why as much as a how! Ain't words fun?!?;P Zinko
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I'm getting the impression I need to hit the books again. :-D Jeremy Falcon
I'm not sure that there is an actual "WHY" for that question of PI's infinite representation (on base 10 numbering, remember that a number has a proper value which is independent of it's representation, and base 10 number representation is a human thing not a natural one). Or even if the question has any meaning. I would however to recall the following saying: "In mathematics we don't really understand things, we just get used to them" This frase has been particularly used in reference to the general concept of infinity, which is not truly understandable by finite creatures like ourselves. Alex
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
This train of thought may also help explain why. The equation for a circle centered about (0, 0) is: R^2 = X^2 + Y^2. I have forgotten how to do it, due to extreme 'un-practice', but I recall that determining the length of an arc requires integrating this in some manner. Search for 'Line Integral' in Google. Therefore, 'C' from 'C = Pi * D' is a rather complicated thing that requires square roots and a whole lot more in order to determine it precisely. It is a lot more complicated than 'sqrt(2)', and as the square root of 2 is a non-repeating number (at least in my memory), pi will be even more convoluted.
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1 / 3 is infinite too ! Any number that cannot be write an integer / 10 ^ some power is infinite. what are you trying to understand? It's also irrational, as pointed out. Could you explain your exact problem? That would help us give you a good solution! ;P
No, 1/3 is not infinite, of course. But written in decimal form instead of fractional form gives an irrational number, namely 1,33333333... -- The Blog: Bits and Pieces
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
- Pi is irrational (P/Q != Pi with P&Q integer) - Pi has infinite number of decimal, but no sequence in its decimal has been found so far (unlike 1/3 = 0.33333...) . . . & the best you can do to understand Pi is to watch Pi, a great movie by Darren Aronofsky.
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
Jeremy, Pi is an irrational number, which means that it cannot be expressed exactly in decimal, nor indeed using any other rational base. It will always have an infinite number of digits following the point. This is because an irrational cannot be expressed as a fraction. There are a number of proofs that Pi is irrational, for example, here: http://pi314.at/math/irrational.html[^]. (I must admit, I don't understand the equations myself - it is a long time since I studied this stuff.) As to *why* Pi is irrational: Mathematics is just wierd like that. Perhaps only God knows. BTW: Sorry to be picky, but Pi is *not* infinite. It is irrational. "Infinity is the state of being greater than any finite (real) number however large." (Wikipaedia). So presumably an "Infinite Number" is a number which is greater than any real number. One of the few things I have learned about mathematics is that it is important to be picky about little differences like this.
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It's not infinite. It's irrational[^]. It can be cranky too if you're not careful. cheers, Chris Maunder
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Super Lloyd wrote:
Could you explain your exact problem? That would help us give you a good solution!
I did. I asked why is Pi infinite. I understand what you said, but that still doesn't address why it is like that - it just reaffirms it's infinite. I'm trying to really understand Pi outside a textbook definition I reckon. Jeremy Falcon
I think that we can say that it is infinte because we can conceptualize us having an infinte amount of time to work it out, just as we can conceptualize us having an infinite amount of time to count. I think that your question "Why is it infinte" has more to do with the nature of infinty than the nature of pi.
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it's not infinite, it's 3.14159265.... infinite is much bigger than that! ;P do you mean never repeat? 1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation. 2nd: yes PI is very special, it's a not even a real such as SQRT(2). Real number (as opposed to rational and integer) are solutino to polynomes equation (e.g. x^2 = 2) No Polynome with real parammters has PI has its solution. (same for 'e' (i.e. 2.7182818...)) they solve an other class of problem altogether...
Super Lloyd wrote:
1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation.
I think you cannot have a never repeating rational number. As you do the long division, at each step you either end up with zero as a remainder (and terminate the sequence) or some other finite positive number. After some number of steps you must have a zero remainder or repeat a previous remainder, at which point you now have a repeating sequence. Robert