the ultimate question: does 0.9999... equal 1

[EcstaticEggplant]

this is wrong though

why?

[Ad Bot]

[Maxwell.]

why?

because it's going entirely off patterns. 3/3 will always = 1 and not just have 0.333 added on from the one before

[The Resonte!]

1/3 is not 0.33333 it's 1/3


on a purely theoretical math level no but if you actually want to use it in real life it's probably better to round it a couple digits up

[Nonnel]

It is literally not equal to 1 but when dealing with more simple things, it's okay to round it to 1.

[EcstaticEggplant]

guys we aren't talking about the actual number 0.9999 or 0.3333, we're talking about it going to infinite.

[SetGaming]

guys we aren't talking about the actual number 0.9999 or 0.3333, we're talking about it going to infinite.

this

[King Tøny]

Only in the movie office space.

[Magus]

Yes, because the difference between them is 0.00000000000 etc., and is therefore infinitely small, which is effectively nothing.

[Red Spy]

scientifically yes
if ur not a frickin nerd no

[Drydess]

1/3 = 0.333....
1/3 + 1/3 + 1/3 = 0.999....

1/3 + 1/3 + 1/3 = 3/3 = 1

0.999... = 1

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

[The Resonte!]

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

lifehack: cut your pie three ways and put them back together for infinite infinitely-thin slices

[Conan]

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

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]

that makes sense

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)