0.999...=1 and why people believe it is false.

[mmmcannibalism]

 

I have to be blunt now, if you cant accept thet .333...=1/3 then your wrong and its impossible to debate this with you.

 

Then why does it continue? It's a representation of 1/3 in decimal form because we cannot achieve 1/3 in this manner.

 

 

 

.999...=1 assumes that 1/3=.333...

 

And .999...=/=1 assumes that 1/3=/=.333...

 

 

 

it continues because manually dividing 1 by 3 gives the result .333...

[kazzin]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

[Riku3220]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

 

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

[mmmcannibalism]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

 

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

 

No, it isn't. Any number of threes added vertically above each other will result in any number of nines. One third can only be represented as a fraction.

 

 

 

so you dont believe 1/3 yields .333...?

 

 

 

If so, its pointless to argue with you.

[kazzin]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

 

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

 

No, it isn't. Any number of threes added vertically above each other will result in any number of nines. One third can only be represented as a fraction.

 

 

 

Every real has an exact decimal representation. People just get confused by the fact that not every real has a unique decimal representation.

[Madmanpur3]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

No, it isn't. Any number of threes added vertically above each other will result in any number of nines. One third can only be represented as a fraction.

Every real has an exact decimal representation. People just get confused by the fact that not every real has a unique decimal representation.

Note the word "representation". 0.999... represents 1, it does not equal 1.

[kazzin]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

No, it isn't. Any number of threes added vertically above each other will result in any number of nines. One third can only be represented as a fraction.

Every real has an exact decimal representation. People just get confused by the fact that not every real has a unique decimal representation.

Note the word "representation". 0.999... represents 1, it does not equal 1.

 

 

 

That's just silly.

[Utopianflame]

As right now I dont feel like typesetting the no number between 0.9... and 1 proof i'm going to stick with saying Cambridge University says 0.9... = 1 and leave it at that.

 

 

 

EDIT: apparently the censor doesnt like Nrich, which is part of Cambridges universities milenium mathematics project.

 

 

 

http://nrich.maths.org/askedNRICH/edited/ 1347 .html

 

 

 

Or you can just go find it (or the many many forums discussions on the same subject there).

[Laura]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

 

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

 

No, it isn't. Any number of threes added vertically above each other will result in any number of nines. One third can only be represented as a fraction.

 

 

 

so you dont believe 1/3 yields .333...?

 

 

 

If so, its pointless to argue with you.

 

If you think you can divide one into three equal parts represented by decmals, it's pointless to argue with you.

I agree. .333... is a third of .999...not 1.

 

 

 

1/3 is a third of one, which cannot be represented in decimal form and is therefore rounded as .333...

[Zierro]

That's just silly.

 

 

 

I think you misunderstand him. By "representation" he doesn't mean they are two things with the same value with different ways of saying them. He's saying they don't have the same value but they both say pretty much the same thing on a calculator (a limited devise), much like how 3.14159265 represents Pi on the calculator but is not Pi precisely.

[mmmcannibalism]

[hide=]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

If 3+3+3= 9, how is .333...+.333...+.333...= any different?

 

Because .333... is 1/3, and 1/3 + 1/3 + 1/3 = 1

 

No, it isn't. Any number of threes added vertically above each other will result in any number of nines. One third can only be represented as a fraction.

 

 

 

so you dont believe 1/3 yields .333...?

 

 

 

If so, its pointless to argue with you.

 

If you think you can divide one into three equal parts represented by decmals, it's pointless to argue with you.

I agree. .333... is a third of .999...not 1.

 

 

 

1/3 is a third of one, which cannot be represented in decimal form and is therefore rounded as .333...

[/hide]

 

 

 

if it cant be represented in decimal form then it must be in irrational number; however, all rational numbers can be expressed as a/b, 1/3 satisfies this so your statement is a contradiction.

[kazzin]

Consider the open interval (0,1) in R.

 

 

 

0.999... is obviously not in this set (0.999... is not an interior point), and thus 0.9... is greater than every number less than 1, and smaller than every number larger than 1. Ergo, 0.9.. = 1

[Powman3]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

[Utopianflame]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

 

 

 

 

Crazy subject maybe, however mathematics isnt subjective(with few exceptions such as the continuum hypothesis), your opinion is wrong and thats a fact.

[kazzin]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

 

Oh, I'm so very sorry sir. I guess you missed all my other posts in this thread.

[mmmcannibalism]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

 

 

for the sake of the discussion then, what is the numerical difference between 1/3 and .333...?

 

mathematics is hardly crazy, its just a matter of learning the material.(and what utopian said)

 

 

 

I do agree kazzin is just being a jerk though

[Riku3220]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

Get a piece of paper and divide 1 by 3 in long division. It will come out to .333... No matter how many time you do it.

 

 

 

1/3 really means 1 divided by 3 so there is no way that 1/3 can't be .333...

[Laura]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

 

 

 

 

Crazy subject maybe, however mathematics isnt subjective(with few exceptions such as the continuum hypothesis), your opinion is wrong and thats a fact.

Why does 1/3 extent by .3 for infinity? Because we cannot reach 1/3 in decimal form. For if we move it one decimal at any given point then it goes over or under. .333... is a third of .999... not 1.

 

 

 

if it cant be represented in decimal form then it must be in irrational number; however, all rational numbers can be expressed as a/b, 1/3 satisfies this so your statement is a contradiction.

 

How is it contradictory?

 

Get a piece of paper and divide 1 by 3 in long division. It will come out to .333... No matter how many time you do it.

 

 

 

1/3 really means 1 divided by 3 so there is no way that 1/3 can't be .333...

You would get infinitely smaller until you reached an insignificant value.

[mmmcannibalism]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

 

 

 

 

Crazy subject maybe, however mathematics isnt subjective(with few exceptions such as the continuum hypothesis), your opinion is wrong and thats a fact.

Why does 1/3 extent by .3 for infinity? Because we cannot reach 1/3 in decimal form. For if we move it one decimal at any given point then it goes over or under. .333... is a third of .999... not 1.

 

 

 

if it cant be represented in decimal form then it must be in irrational number; however, all rational numbers can be expressed as a/b, 1/3 satisfies this so your statement is a contradiction.

 

How is it contradictory?

 

Get a piece of paper and divide 1 by 3 in long division. It will come out to .333... No matter how many time you do it.

 

 

 

1/3 really means 1 divided by 3 so there is no way that 1/3 can't be .333...

You would get infinitely smaller until you reached an insignificant value.

 

 

 

1/3 is .3 forever because basic division proves it; .999... is 1 because its 3 times 1/3 which equals 1

 

 

 

its contradictory because any rational number can be represented in the form a/b; .333... is not irrational because it repeats yet you are saying there isnt a fractional form for it.

[Utopianflame]

Laura it is a result in number theory that any infinite recurring decimal is a rational number. EDIT : http://www.cs.uiowa.edu/~fleck/ratnote.pdf its explained and proved here.

 

 

 

In the case of 0.3... that rational number is 1/3.

 

 

 

Rocco, x= infinity is invalid notation, its against the rules of mathematics.

[Laura]

1/3 is .3 forever because basic division proves it; .999... is 1 because its 3 times 1/3 which equals 1

 

 

 

its contradictory because any rational number can be represented in the form a/b; .333... is not irrational because it repeats yet you are saying there isnt a fractional form for it.

That assumes the 1/3 equals .333... which it cannot; 1/3 is almost negligibly more accurate. 1/3 is represented as .333... because 1/3 cannot be achieved. It's represented by what we can all agree is near equivalent. That law can go on to assume what we assume. I'm not saying it isn't represented, but that it cannot be represented in the accuracy that 1/3 can.

[Zierro]

Crazy subject maybe, however mathematics isnt subjective(with few exceptions such as the continuum hypothesis), your opinion is wrong and thats a fact.

 

 

 

He said no one knows the answer, he didn't say there is no answer. He's right. Who's to say you're more right than us? Only a perfect being could prove who is right and who is wrong... and none of us have that attribute.

[Utopianflame]

Crazy subject maybe, however mathematics isnt subjective(with few exceptions such as the continuum hypothesis), your opinion is wrong and thats a fact.

 

 

 

He said no one knows the answer, he didn't say there is no answer. He's right. Who's to say you're more right than us? Only a perfect being could prove who is right and who is wrong... and none of us have that attribute.

 

 

 

In this case i'm a mathematics graduate (0.9... = 1 was actually covered in analysis), and a great many answers in mathematics are known and proven, they are called theorems. Its a construction entirely of logic, when something is proven it stays that way. Nothing can overturn it.

[Powman3]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

Get a piece of paper and divide 1 by 3 in long division. It will come out to .333... No matter how many time you do it.

 

 

 

1/3 really means 1 divided by 3 so there is no way that 1/3 can't be .333...

 

 

 

That makes sense, why didn't I think about that?

[Laura]

Seriously. If you don't think 1/3 = 0.3... then you probably should've paid more attention back in 4th grade when you were learning long division.

 

 

 

How about instead of joining just to be an annoyance and a jerk you could actually pitch in the conversation?

 

 

 

And in my honest opinion, I think 1/3 =/= .333.... Mathematics is a crazy subject that no one knows the right answers in.

 

 

 

 

 

Crazy subject maybe, however mathematics isnt subjective(with few exceptions such as the continuum hypothesis), your opinion is wrong and thats a fact.

Facts can be true or false.

 

Nothing can overturn it.

 

I detest.