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the ultimate question: does 0.9999... equal 1
PhantOS:
also any number less than 9 as the numerator in a fraction over 9 will be equal to 0.xxxxx or whatever that number is right
so 8/9 = 0.888888...
9/9 would not equal 0.999... but actually 1 because any number over itself is always 1
Maxwell.:
--- Quote from: Aide33 on March 18, 2017, 04:03:14 PM ---you must not believe in calculus then
--- End quote ---
do you mind elaborating on that cause I'm genuinely curious
Crazy Salt:
1/3 = 0.333....
1/3 + 1/3 + 1/3 = 0.999....
1/3 + 1/3 + 1/3 = 3/3 = 1
0.999... = 1
Mega-Bear:
In calculus when dealing with a limit at 1, it is appropriate to sometimes treat 0.9999... as 1 because a function can get infinitely close to 1, but as long as that limit's there, it will never fully achieve 1. But we still need to occasionally do work with 1, so we substitute 0.9999... instead.
However if we look at this from a chaotician's perspective, differences in starting conditions may lead to enormous differences in a system farther down the line, (source: Jurassic Park) therefore treating 0.9999... and 1 as equal can be dangerous.
It is all about context.
Maxwell.:
--- Quote from: Mega-Bear on March 18, 2017, 05:08:26 PM ---In calculus when dealing with a limit at 1, it is appropriate to sometimes treat 0.9999... as 1 because a function can get infinitely close to 1, but as long as that limit's there, it will never fully achieve 1. But we still need to occasionally do work with 1, so we substitute 0.9999... instead.
However if we look at this from a chaotician's perspective, differences in starting conditions may lead to enormous differences in a system farther down the line, (source: Jurassic Park) therefore treating 0.9999... and 1 as equal can be dangerous.
It is all about context.
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that makes sense
--- Quote from: Crazy Salt on March 18, 2017, 05:06:56 PM ---1/3 = 0.333....
1/3 + 1/3 + 1/3 = 0.999....
1/3 + 1/3 + 1/3 = 3/3 = 1
0.999... = 1
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this is wrong though