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## Does 0.9999(repeating) = 1?

Yes 705 56.9%
No 578 46.65%
Voters 1239 .

### Does 0.9999(repeating) = 1?

IS14696195e1336cdef530a

Senior Member

anyway endless*2 being as big as endless*1 makes sense in some way
because 0*2 is 0 and 0*1 is 0 so endless is basically the opposite of `zero or what? :3

Kodoku

Senior Member

Quote:
Every number has a unique infinite decimal expansion, well known theorem of the reals.
Only if you exclude certain decimal expansions. http://en.wikipedia.org/wiki/Decimal_representation#Non-uniqueness_of_decimal_representation (http://na.leagueoflegends.com/board/redirect.php?do=verify&redirect_url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FDecimal_representation%23Non-uniqueness_of_decimal_representation)
Quote:
My question is 1+1=2 0.99...+0.99.... is that equal 2 then ?? or equal 1.99........ and then theoretically end with an 8, even though its endless and dont end :P also is the number 999.... =100..... ?
0.99...+0.99... is indeed 2. It is also 1.99..., but no 8s. If you look at the nth decimal slot in the decimal expansion of the product of 0.99... and 0.99..., you'll see that it's the sum of 1 (from 9x9 = 81) and 8 (carried over from the 9x9 = 81 from the n+1th slot). As for 99... and 100..., those are simply not numbers.

Riot Morgageddon

Player Support Tech Specialist

Quote:
Kaolla:
*in our currently accepted decimal form.

1/9 = .111 R1/9 in my handy extended notation

9 x 1/9 = 9 x .111 R1/9 = .999 R9/9 = 1

ain't it a thing of beauty? no approximation, just clean EXACT math

If you want to write a fraction as a decimal approximation, why are you reverting back to using fractions in it?
There's no point in writing it as a decimal if you're going to use the fraction as a part of the equivalent expression.

That's like saying 5 and 2/3rds is 5 R 2/3 in your way.

Kaolla

Senior Member

Quote:
Morgageddon:
If you want to write a fraction as a decimal approximation, why are you reverting back to using fractions in it?
There's no point in writing it as a decimal if you're going to use the fraction as a part of the equivalent expression.

That's like saying 5 and 2/3rds is 5 R 2/3 in your way.

because .333 R 1/3 actually denotes that what you're looking at is a number where .333 is a process

i can use .333 R 1/3 in other operations. i can't use .333

Riot Morgageddon

Player Support Tech Specialist

Quote:
Kaolla:
because .333 R 1/3 actually denotes that what you're looking at is a number where .333 is a process

i can use .333 R 1/3 in other operations. i can't use .333

you can use .333 in any process. The question is when you know to cut it off, simple reasoning skills.

I need to make a joist that's 10 feet long, 4 inches and 1/3rd. Can I have a snug fit as .3? Probably. Is .33 going to make it even more precise and snug? Sure. Can I cut that? With laser length table saws, sure. Then why not .333? Ok, you're going to need a professional table saw now. .3333? Industry might have a saw for you.

You're missing the entire point of the matter. If you can't know when you have enough data, enough resolution to make your equations accurate, then you shouldn't be worrying about it in the first place.

Dobagoh

Member

Quote:
Crowcide:
All of the arguments about decimal fraction representation or setting x = .999~ are essentially circular arguments. .999~ = 1 cause of definition no other reason.

You are one dumb mother fucker.

Kaolla

Senior Member

Quote:
Morgageddon:
You're missing the entire point of the matter. If you can't know when you have enough data, enough resolution to make your equations accurate, then you shouldn't be worrying about it in the first place.

and YOU don't understand that when we say EQUAL in math, we don't mean "good enough that you're going to have a seriously hard time telling the difference" we really do mean equal.

it's complete wanking and a waste of time, but infinitely small differences are still differences in math

Senior Member

The truth is that .999 repeating isn't real, just as teemo isn't real. They are ideas.

Crowcide

Senior Member

Quote:
Dobagoh:
You are one dumb mother fucker.

Yup I'm clearly the dumb one with a masters in math talking about math, not the guy who has no clue what he's talking about.