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## Does 0.9999(repeating) = 1?

Yes 705 56.9%
No 578 46.65%
Voters 1239 .

### Does 0.9999(repeating) = 1?

Kaolla

Senior Member

Quote:
Peacë:
I believe the Answer is A

could be either, as the game doesn't let you put a portal on a moving surface

i'd probably go with B though, since the game does display the transferal of momentum of objects going through, and the cube is going through the portal at a specific rate of speed regardless of it being stationary or the portal being stationary.

i guess we'll need to build it in order to verify.

we've got a lot of work to do, let's get started. you monster

Kaolla

Senior Member

changed my mind to A after some meditation

Senior Member

Quote:
Griftrix:
Could those who do not believe it is the same number please post your highest degree of math? Mine is post graduate.

Appeal to authority, nice.

Hey I hate to break this to you, but Albert Einstein thought the universe was static at one point. He later abandoned this idea and called it the biggest blunder of his career.

Cool Stuffz

Senior Member

Quote:
Appeal to authority, nice.

Hey I hate to break this to you, but Albert Einstein thought the universe was static at one point. He later abandoned this idea and called it the biggest blunder of his career.

So, what you're saying is that he made a mistake and corrected it?

Perhaps you should do the same regarding .999...=1

Senior Member

Quote:
larryjerry1:
So, what you're saying is that he made a mistake and corrected it?

Perhaps you should do the same regarding .999...=1

I'm saying a post-graduate degree doesn't mean anything, in-and-of itself. Other than you sat around through school for a long time.

What you can prove or disprove is what matters. Thanks for the downvote, but I'm still right.

mwarme

Senior Member

Ok... So i'm just gonna lay this out here. Aside from my issue with the 1/3 = .3(bar) proof, which is flawed because it assumes .3(bar) accurately represents 1/3, the other most common proof is the limits:

take the standard representation of .9(bar) to be the sum of an infinite geometric series, (sigma i=0 to infinity) 9/(10^i). Thus, we have a series of terms 9/10 +9/100 + 9/1000 + 9/10000 .... +9/(10^n)

Easily rewritten as .9 + .09 + .009 + .009 + ... + 9 x 10^(-n)

Given this proof, we take the limit as n approaches infinity to be 1. Here's the kicker. It's the LIMIT as n APPROACHES infinity. Two key points here, from any collegiate calculus textbook:

#1. by the definition of the limit, 1 is the value that it approaches, but does not ever technically reach. concept of an asymptote anyone?

#2. we APPROACH infinity. We never get there. We thusly assume we will always deal with approximations any time we attempt to get a numerical solution. .9(bar) is a numerical solution for the sum of the infinite series 9/(10^n), but it is NOT an appropriate analytic solution.

Now, for all intents and purposes, we can use .9(bar) as one. You need a higher level of pure math than I have taken as a numerical analysis major (math track for computer geeks) to even get into realms where .9(bar) does not equal 1 for all reasonable uses. However, I can tell you if you try that **** with floating point arithmetic, you WILL NOT get one. 3 x .3(bar) does not = 1 in double precision floating point arithmetic, it returns .999999999999999999999..i'm leaving off some, but whatever the precision is of your floating point, it doesn't return one.

Gloved Thief

Junior Member

1/3= .9
3/3= 1
thus, 1/3 x 3 = 1

mwarme

Senior Member

Quote:
nlewman:
1/3= .9
3/3= 1
thus, 1/3 x 3 = 1

1/3 = .9 is not a step i've seen anywhere, and I don't think anyone would try to defend that. Anyway, This proof assumes that 1/3 = .3(bar) accurately represents the value of 1/3. This proof attempts to use the conjecture as a proof of itself. Logical fallocy. Sugar is sweet because sugar is sweet. Makes no sense.

MiziiziM

Senior Member

Quote:
Mèdusa:
0.9999.... = X
10 X = 9.999....
10X - X = 9
9X = 9
9X / 9 = 1
So, X = 1

That's the standard proof anyway

This is wrong.

10x - x =/= 9

10x - x = 9x

Then you assumed that 9x is equal to 9 without any proof, so the rest of this is wrong as well.

Spirited Warrior

Member

Quote:
Mèdusa:
0.9999.... = X
10 X = 9.999....
10X - X = 9
9X = 9
9X / 9 = 1
So, X = 1

That's the standard proof anyway

That is wrong. Think about it, if that is true then any number will work.
example.

10 X = 7.777....
10X - X = 7
7X = 7
7X / 7 = 1
So, X = 1