PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
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From: David R Tribble on 13 Jul 2010 20:08 K_h wrote: > This is wrong. Consider PI = 3.1415... and note that its first digit is a 3, its > second digit is a 1, its third digit is a 4, and so on. There are various > formulas that allow one to calculate ANY of its ALEPH_0 digits. But those > formulas take time to compute and so many, in fact infinitely many, of its digits > can't be calculated by humans -- unless some breakthrough happens in pure theory > that allows one to calculate the nth digit of PI by some simple but clever > formula f(n). You can calculate the nth hexadecimal (or binary) digit of' pi in O(1) time: http://en.wikipedia.org/wiki/Digits_of_pi#Digit_extraction_methods http://en.wikipedia.org/wiki/Bailey-Borwein-Plouffe_formula
From: Nam Nguyen on 13 Jul 2010 22:18 Marshall wrote: > On Jul 12, 7:19 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> K_h wrote: >>> "Nam Nguyen" <namducngu...(a)shaw.ca> wrote in message >>> news:uNc_n.6705$KT3.5193(a)newsfe13.iad... >>>> K_h wrote: >>>>> "Nam Nguyen" <namducngu...(a)shaw.ca> wrote in message >>>>> news:MTSZn.2663$Bh2.125(a)newsfe04.iad... >>>>>> K_h wrote: >>>>>>> Mathematical truth exists. >>>>>> Sure. In your mind for example! >>>>> And also outside of the human mind. >>>> Did you mean _physically outside of human mind_ ? That's very bizarre to say >>>> of mathematical abstractions that human thinks of. No? >>> The truth underlying the abstractions does exist. >> Sure. In your mind for example! >> >> >> >>> No, I correctly claimed that the truth underlying regular arithmetic does exist >>> and that truth is independent of context. 1+1=2 is true for any two objects: two >>> cars, two houses, two people, etc. >> But 1+1=2 is true in many ... many _modulo arithmetics_ "for any two objects: two >> cars, two houses, two people, etc.", right? > > That's a different plus. So, how many _different_ pluses can you see in 1+1=2? You see, the truth of "1+1=2" is subjective, relative to what different meanings you or anybody else would take '+' to mean. Your "a different plus" actually confirms, not denies, the relativity of mathematical truth here! > > So your whole argument about "relativity" reduces to pointing out that > sometimes words mean different things, like when "blue" can mean > a particular color, or an emotion, or "marked by blasphemy." In a nutshell yes. As you yourself said "That's a different plus"! > Your > only *technical* point about "no absolute truth" is that there is no > absolute authoritative definition. Your "authoritative definition" here in this context is obscured. > Whoop de do! What an amazing thing you've discovered! It's actually quite trivial: you yourself discovered it in _your_ "That's a different plus"! -- --------------------------------------------------- Time passes, there is no way we can hold it back. Why, then, do thoughts linger long after everything else is gone? Ryokan ---------------------------------------------------
From: Marshall on 14 Jul 2010 00:40 On Jul 13, 7:18 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > > So your whole argument about "relativity" reduces to pointing out that > > sometimes words mean different things, like when "blue" can mean > > a particular color, or an emotion, or "marked by blasphemy." > > In a nutshell yes. As you yourself said "That's a different plus"! > > > Your > > only *technical* point about "no absolute truth" is that there is no > > absolute authoritative definition. > > Your "authoritative definition" here in this context is obscured. > > > Whoop de do! What an amazing thing you've discovered! > > It's actually quite trivial Yes. All this stuff about relativity you've been saying is trivial and obvious, as I've said before. Marshall
From: Nam Nguyen on 14 Jul 2010 00:44 Marshall wrote: > > Yes. All this stuff about relativity you've been saying > is trivial and obvious Yes, The principle of it is very similar if not identical to SR, which I'm sure you studied before. Did you not? Why have you seemed to have problem understanding it now? -- --------------------------------------------------- Time passes, there is no way we can hold it back. Why, then, do thoughts linger long after everything else is gone? Ryokan ---------------------------------------------------
From: Tim Little on 14 Jul 2010 01:50
On 2010-07-14, David R Tribble <david(a)tribble.com> wrote: > You can calculate the nth hexadecimal (or binary) digit of' pi > in O(1) time: > http://en.wikipedia.org/wiki/Digits_of_pi#Digit_extraction_methods > http://en.wikipedia.org/wiki/Bailey-Borwein-Plouffe_formula Those algorithms typically run about O(n) time(*). The really interesting thing about them is that they use O(1) space(*), so that you can get the trillionth digit without having to operate on trillion-digit numbers. They're also trivially parallelizable. (*) Technically slightly higher as integer arithmetic is generally not considered to be O(1). - Tim |