so i waz reading this book on diff geomatry and look what it said
"evry numbr t 0<t<=1 can be representd by an infinte decimal (even 1 :O) t = 0,c1c2...cn...
fr exampol 1/8=0.125=0.1249999... k let cn1, cn2 be non-vnishing digitz
the image point t is point 0< x1,x2 <=1
x1=0.c1...cn1cn2+1...cn3... , x2=0.cn1+1...cn3cn3+1... so maping is 1to1
for example x1=0.04601..., x2=0.7000302... has inverse image t=0.047600030102... but im not sure i follow where t cumz from it doesnt seem to follow its patern earlier? can anyone break the digits t down into the corresponding cns and stufs? thx
People don't have any fucking trouble with the fractions, but as soon as you make clear use of the repeating decimals of those SAME fractions, they get their knickers in a twist, and there's no need for it, since it's equally true:
0.333... + 0.666... = 0.999...
Therefore:
0.999... = 1
Name:
Anonymous2008-04-23 9:24
0.999... + 0.000...1 = 1
Suppose 0.999... = 1 and subtract from both sides, then we get:
0.000...1 = 0
Contradiction.
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sage2008-04-23 11:22
>>6
I think the problem with that argument is that the normal rules for carrying digits in addition don't really apply.
0.999... + 0.000...1 doesn't necessarily add up to 1 because you can't assume that carrying digits to get the right answer will hold true. Maybe I'm full of shit here. Anyone care to back me up?
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Anonymous2008-04-23 12:28
>>7
Yeah, >>6 is a bollocks way of explaining it, but not a bad way of thinking about it. If 0.999... and 1 are two distinct real numbers, then there must exist a number x that is their difference. But since 0.999... + x is greater than 1, no matter how small x is, we conclude "obvious bullshit".
>>10
Correct. >>6 is an assfagging cockmilker who only pretends to understand the maths. There is no such thing as 0.000...1 for the reason you well stated. >>6 has to go back to burping more sperm and slurping more shaft.
but OP is saying that any number can be represented as an infinite expression and that given two numbers (expressed in terms of infinite repeating) there exists one repeating number to "map" two numbers to. Is this true?
>>17
Every pair of coordinates on the Cartesian plane produces a unique point. One "corresponding" number doesn't carry enough information to produce that uniqueness. Hence, the Cartesian plane cannot be represented with a set of single numbers. Now do a barrel roll.
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Anonymous2008-04-24 19:01
>>18
Well the cardinality of RxR is c, so that really implies that there is an injection from RxR into R. So in fact you're wrong.
Totally wrong.
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Anonymous2008-04-24 19:40
>>18
Bitches don't know about my space filling curve.
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Anonymous2008-04-24 19:52
>>20
omg thats the pictr in the book :D thx alot mr 20
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Anonymous2008-04-26 15:22
>>18
This should be bumped for how stupid redcream looks
>>22
Are you seriously suggesting we continuously bump every thread in which redcream posts misinformation or a logical fallacy? We already have one thread for that on the mainpage, & this board is unproductive enough with him here as it is.