PROOF INFINITY DOES NOT EXIST! Not even ONE type
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From: |-|ercules on 6 Jul 2010 15:23 > does Champernowne's constant contain pi? It does contain all finite digit > sequences of pi. > > - Tim C10 = 0.12345678910111213141516... It contains pi, segmented. You have to stop thinking of infinity as a really long string for a moment, because there's no infinite string of pi inside root 2 or e etc. but the further you go along the string the longer and longer sequences are found. ----------------------------------------------- 1/ there's no infinite sequence of pi's digits within C10 (every finite starting point has a finite ending point) 2/ as the length of C10 digit expansion -> oo, the consecutive number of digits of pi -> oo 3/ the length of C10 digit expansion is oo 4/ the consecutive number of digits of pi = oo (3) -> (2) CONTRADICTION (1) & (4) THEREFORE no limit exists as the length of digit expansions (of any real) -> oo GENERALIZATION no limit exists as the length of sequences (of any type) -> oo INFERENCE there is no oo Herc -- Conan do we REALLY have to hear the lamentations of the women?
From: |-|ercules on 8 Jul 2010 20:43
A REVISED PROOF OF THE NON-EXISTENCE OF INFINITY C10 = 0.12345678910111213141516... x = the number of digits in the expansion of C10 y = the number of consecutive digits of PI in C10 As x->oo, y->oo x = oo Assume the limit exists. y=oo Contradiction (for each finite starting digit of PI in C10 there is a finite ending digit) Limit doesn't exist. y cannot reach infinity therefore x cannot reach infinity x = the number of digits in the expansion of C10 x =/= oo > > INFERENCE there is no oo > > Herc > -- > Conan do we REALLY have to hear the lamentations of the women? |