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


tryto

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So, what is 1.111... equal to?

 

10/9.

 

 

 

Please don't continue.

 

 

 

I'm only bumping this because I forgot about this thread.

 

 

 

That didn't really answer my question, you know.

 

 

 

10/9 = 1.111...

 

 

 

1.111 * .9 = .999...

 

 

 

Therefore, 1.111... = 1 = .999...?

 

 

 

<_<

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So, what is 1.111... equal to?

 

10/9.

 

 

 

Please don't continue.

 

 

 

I'm only bumping this because I forgot about this thread.

 

 

 

That didn't really answer my question, you know.

 

 

 

10/9 = 1.111...

 

 

 

1.111 * .9 = .999...

 

 

 

Therefore, 1.111... = .999...?

 

 

 

<_<

 

 

 

#-o (I was going to look up a facepalm picture but am too lazy).

 

 

 

I know you'll need an explanation:

 

1.11... = 10/9

 

.9 = 9/10

 

10/9 * 9/10 obviously equals one. How you thought the "Therefore 1.11...=.99..." was the next part I have no idea.

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10/9 = 1.111...

 

9/10 = .9

 

10/9*9/10 = 1

 

1.111...*0.9 = .999...

 

10/9*9/10 = 1.111*0.9

 

1 = .999...

 

 

 

Seriously. Try to prove .999... = 1 wrong.

I shall take my flock underneath my own wing, and kick them right the [bleep] out of the tree. If they were meant to fly, they won't break their necks on the concrete.
So, what is 1.111... equal to?

10/9.

 

Please don't continue.

wm1c2w.jpg

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So, what is 1.111... equal to?

 

10/9.

 

 

 

Please don't continue.

 

 

 

I'm only bumping this because I forgot about this thread.

 

 

 

That didn't really answer my question, you know.

 

 

 

10/9 = 1.111...

 

 

 

1.111 * .9 = .999...

 

 

 

Therefore, 1.111... = .999...?

 

 

 

<_<

 

 

 

#-o (I was going to look up a facepalm picture but am too lazy).

 

 

 

I know you'll need an explanation:

 

1.11... = 10/9

 

.9 = 9/10

 

10/9 * 9/10 obviously equals one. How you thought the "Therefore 1.11...=.99..." was the next part I have no idea.

 

 

 

I don't need an explanation. I'm not that dumb, and I wasn't being totally serious with the whole 1.111 = .999 thing (Hence the "<_<" at the end). In my initial question, I asked what 1.111... was equal to and I got 10/9, which is about as helpful as saying 9/9 equals one. It's assumed that every non-repeating number has an equivalent which can be expressed with 9's (i.e., .8904 = .89039...), right? Well, I was simply asking how that would rule be replied in reverse (i.e., what's the equivalent to a repeating number which doesn't end in 9's).

 

 

 

A fairly simple question :P

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The answer to that is yes. 1.01 = 1.0999... , 6743.843 = 6743.842999... etc.

I shall take my flock underneath my own wing, and kick them right the [bleep] out of the tree. If they were meant to fly, they won't break their necks on the concrete.
So, what is 1.111... equal to?

10/9.

 

Please don't continue.

wm1c2w.jpg

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The answer to what's the equivalent of 1.111... is "yes"? o_O

 

...it's 10/9, what more do you want? Nevermind, there's no point continuing.

 

 

 

I'll just copy and paste what I wrote out earlier.

 

 

 

It's assumed that every non-repeating number has an equivalent which can be expressed with 9's (i.e., .8904 = .89039...), right? Well, I was simply asking how that would rule be replied in reverse (i.e., what's the equivalent to a repeating number which doesn't end in 9's).

 

 

 

Saying that 1.111... = 10/9 is dumb, because no one is asking what 1.111... expressed in fractions is, as everyone knows what it is expressed in fractions. That's not what I was asking. Sheesh. I mean, I know the answer to the question. Do you?

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The answer to what's the equivalent of 1.111... is "yes"? o_O

 

...it's 10/9, what more do you want? Nevermind, there's no point continuing.

 

 

 

I'll just copy and paste what I wrote out earlier.

 

 

 

It's assumed that every non-repeating number has an equivalent which can be expressed with 9's (i.e., .8904 = .89039...), right? Well, I was simply asking how that would rule be replied in reverse (i.e., what's the equivalent to a repeating number which doesn't end in 9's).

 

 

 

Saying that 1.111... = 10/9 is dumb, because no one is asking what 1.111... expressed in fractions is, as everyone knows what it is expressed in fractions. That's not what I was asking. Sheesh. I mean, I know the answer to the question. Do you?

 

 

 

Good grief. There is no eternal 9 ending to what 1.111... equals. Because all there is an infinate amount of 1's.

I shall take my flock underneath my own wing, and kick them right the [bleep] out of the tree. If they were meant to fly, they won't break their necks on the concrete.
So, what is 1.111... equal to?

10/9.

 

Please don't continue.

wm1c2w.jpg

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Hmm I found it funny that I put 0.99999999999999999999999999999999999999 * 1 in a graphing calculator and the answer was 1.

 

 

 

Graphing calculators usually round to the 8th decimal place or so.

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0.999... is equal to one, its very simple. You just can't think of 0.999... as a "number" per se.

 

 

 

People are used to numbers like 4, 2, 193.82, and so forth

 

Then you have 'number' like 0.333... people think of this as the number 0.3 followed by a million 3's. This is misleading. The written expression 0.3333... isn't a number like that, 0.3333... is one third. Yes when you write it you use numbers, but its not really a integer, its the way of writing 1/3 using a decimal.

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Well, not only that, any number that doesn't terminate or repeat is an irrational number, isn't it?

 

I believe so. A number that cannot be represented as a fraction, does not terminate, or does not repeat. Such as pi.

 

 

 

[hide=Thanks Wikipedia]*The ratio of the hypotenuse to an arm of an isosceles right triangle is a:b expressed in the smallest units possible.

 

*By the Pythagorean theorem: a^2 = 2b^2.

 

*Since a^2 is even, a must be even as the square of an odd number is odd.

 

*Since a:b is in its lowest terms, b must be odd.

 

*Since a is even, let a = 2y.

 

*Then a^2 = 4y^2 = 2b^2

 

*b^2 = 2y^2 so b^2 must be even, therefore b is even.

 

*However we asserted b must be odd. Here is the contradiction[/hide]

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