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| the ultimate question: does 0.9999... equal 1 |
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| The Resonte!:
--- Quote from: Drydess on March 18, 2017, 07:36:11 PM --- 1/3 + 1/3 + 1/3 does not equal 0.9999..., it equals 1 when you cut a pie three ways you don't end up with a microscopic sliver, you just end up with three pieces --- End quote --- lifehack: cut your pie three ways and put them back together for infinite infinitely-thin slices |
| Conan:
--- Quote from: Drydess on March 18, 2017, 07:36:11 PM --- 1/3 + 1/3 + 1/3 does not equal 0.9999..., it equals 1 when you cut a pie three ways you don't end up with a microscopic sliver, you just end up with three pieces --- End quote --- except 0.999999... is 1 which is the whole point of that proof but yeah its not the commonly accepted way to prove it as it is prone to counterarguments due to fraction conversion to decimal and such. phantos' way is the commonly used indisputable way. |
| Aide33:
--- Quote from: Maxwell. on March 18, 2017, 05:09:51 PM ---that makes sense --- End quote --- Calculus uses the infinitesimal and builds off of this to derive integrals, differentiation, limits, etc. the way newton derived everything was by making the assumption that dy = 0 and dx = 0 as two points on a graph get closer and closer effectively, by doing 0.99999... you infinitely get closer and closer to 1, so we can say the limit of 1-dx as dx approaches 0 is 1. infinitesimals where a very controversial part of mathematics for a long time since certain mathematicians didn't believe in infinitely small parts of an object, for example in the physical world, you cant divide an atom forever since matter cannot be smaller than Planck's constant. But in math, you can, since it's all in your head. for more info: https://en.wikipedia.org/wiki/Infinitesimal |
| Nonnel:
i suppose the opposite of 0.9999999... is 0.0000000... and if the 9s repeat forever, then the 0s must also repeat forever. if it keeps on going to infinity, it will never end with "...00001" so 0.9999... is equal to 1. |
| TableSalt:
Okay, so is this 0.999... (infinite 9s here) ...999 or is it 0.999... (infinite 9s here, with no literal end) |
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