0.999... = 1 debate

[hunter1801]

This part of the forum has seen more lively days, so I figured I'd bring this here. Hopefully it gets views.

Alright, so I'll start off by saying that I do in fact believe that 0.999...(repeating) is = to 1. They are the same thing.

If you don't believe the idea that 0.999...=1 just read up a little here:
http://en.wikipedia.org/wiki/0.999...

Or google for proofs.

My ACTUAL question, or reason for this topic, is for someone to help me prove this to people who come back with the question of dividing a pie into equal portions. For example, I can tell someone the above is true, and mathematically prove it, but if they ask something like, "If I have 1 pie and I want to divide it equally for 9 kids, how much do I give each kid?" I can't answer it. Mathematically it comes to 11.111...% for each kid, which is is 0.111... which SHOULD be 1, but makes no sense in this form.

So ya, thoughts?

[Hardware Junkie]

Realistically you wouldn't. Some pieces of the pie would be smaller or larger depending.
Unless you cut your pie with a laser, a microscope and a computer to make the necessary calculations.

[evasive]

it is not 1. However small the difference (going NEAR zero but NEVER reaching zero) there is a difference.

[hunter1801]

it is not 1. However small the difference (going NEAR zero but NEVER reaching zero) there is a difference.

then how would you argue against:

1/3 = 0.333...
3 x 1/3 = 3 x 0.333...
1 = 0.333...

or

x=0.999...
10x=9.999...
10x-x= 9.999... - 0.999...
9x=9
x=1

or any of the other proofs that the numbers are equal

[Roach412]

then how would you argue against:

1/3 = 0.333...
3 x 1/3 = 3 x 0.333...
1 = 0.333...

or

x=0.999...
10x=9.999...
10x-x= 9.999... - 0.999...
9x=9
x=1

or any of the other proofs that the numbers are equal

simply by stating fractions are not always truly decimals and decimals are not always truly fractions. their inter-use is a convenience for us - but doesn't account for their actual exact value.

makes sense to me?

-Roach

[Roach412]

as a side-note....

a friend of mine, brilliant math genius, did a proof showing -1 = 1, basically as long as you accept that 0 has value.

chew on that fat for a while.

it goes along the same thought lines as 0.9999...., since you still need to make assumptions as to how you define value.

-Roach

[hunter1801]

then how would you argue against:

1/3 = 0.333...
3 x 1/3 = 3 x 0.333...
1 = 0.333...

or

x=0.999...
10x=9.999...
10x-x= 9.999... - 0.999...
9x=9
x=1

or any of the other proofs that the numbers are equal

simply by stating fractions are not always truly decimals and decimals are not always truly fractions. their inter-use is a convenience for us - but doesn't account for their actual exact value.

makes sense to me?

-Roach

The second example doesn't use fractions.

Oh and I doubt he had an actual WORKING proof for -1 = 1. More than likely he used a known proof involving square roots and the use of "i" that has a fallacy in it.

[Roach412]

The second example doesn't use fractions.

Oh and I doubt he had an actual WORKING proof for -1 = 1. More than likely he used a known proof involving square roots and the use of "i" that has a fallacy in it.

the second one still makes you believe in an assumption which makes an infinitely repeated value have a finite value. you can never add or subtract a infinitely repeated number by any other number. whether you "believe" otherwise is moot...it's impossible as the number's value doesn't exist until you end it, at which point it's not longer a repeating number.

as for the proof...i have no idea. he's too smart for his own good. he finished college math through weekly tests and correspondences by the time he was 15, received a full-ride scholarship to chicago's illinois institute of technology, and triple majored there in 4 years summa cum laude. he's been working for microsoft for a number of years now. brilliant guy...strange, but brilliant. he did that proof while on a family trip when we were still in middle school.

-Roach

[hunter1801]

the second one still makes you believe in an assumption which makes an infinitely repeated value have a finite value. you can never add or subtract a infinitely repeated number by any other number. whether you "believe" otherwise is moot...it's impossible as the number's value doesn't exist until you end it, at which point it's not longer a repeating number.

-Roach

So then I guess you would be able to disprove the mathematicians that have provided research and proof of this concept for centuries. I don't see why you wouldn't be able to subtract or add infinite numbers. Numbers aren't a "process". It isn't like 0.xxx... is repeating over time. Written numbers are just symbols we use to represent a concept. 0.xxx... - 0.xxx... = 0 since you are subtracting two identical numbers.

On a side not, I'm not a high level math major or anything. Just a regular ol' business major. My questions and opinions are just what I see and understand based on what I read.

[Roach412]

So then I guess you would be able to disprove the mathematicians that have provided research and proof of this concept for centuries. I don't see why you wouldn't be able to subtract or add infinite numbers. Numbers aren't a "process". It isn't like 0.xxx... is repeating over time. Written numbers are just symbols we use to represent a concept. 0.xxx... - 0.xxx... = 0 since you are subtracting two identical numbers.

On a side not, I'm not a high level math major or anything. Just a regular ol' business major. My questions and opinions are just what I see and understand based on what I read.

the point is, these proofs require assumptions that must be accepted in order for the desired outcome to happen. if you don't "believe" in the assumption, then the proof is invalid. if you do believe in the assumption, then it is valid.

my point still remains, until you DEFINE the final value of a repeated number, you don't have a real number by which to do calculations from. they will never be the same, as their value can always be adjusted by repeating the number again...and again...and again... fractals are similar example.

0.9... could be: 0.9999999999999999999999999999999
0.9... could be: 0.999999999999999999999999999999
they can be any variation of these, more 9's fewer 9's...doesn't matter. until you say "there! that's how many 9's there are", you simply do not have a real number from which to do equations with - it's an undefined limit. you only have a number in theory - hence a proof that requires an accepted assumption.

if you do not make a point at which the number ends, then yes, it really does not end - ever...over any amount of time space or anything. it quite literally is a race to infinity. it is not a defined number, and therefore cannot be used in a REAL equation - unless you accept an assumption. in my case, i'm not accepting the assumption - so it doesn't. in your case, you are accepting the assumption - so it works.

right now i just decided to accept the assumption, i agree, it works.

i now refuse the assumption, it doesn't work.



i'm also by no means a mathematician - far from it. i am however a logic addict. the above comes simply from my understanding of math theory, and my interpretation of it through my understanded/applied logic.

-Roach