.9 Repeating = 1 YES -or- NO

[ericnkatz]

Again i would like to quote my dr math friend Dr. Ian

This is a letter from 2 girls with this very problem of understanding, please read it.. It is generally excepted that

1 = .999 [repeating]

Date: 03/21/2001 at 16:22:11

From: Doctor Ian

Subject: Re: .999999..... I still don't get it

Hi Emily and Jenny,

There's no doubt that this equality is one of the weirder things in

mathematics, and it _is_ intuitive to think: No matter how many 9's

you add, you'll never get all the way to 1.

But that's how it seems if you think about moving _toward_ 1.? What if

you think about moving _away_ from 1??

That is, if you start at 1, and try to move away from 1 and toward

0.99999..., how far do you have to go to get to 0.99999... ?? Any step

you try to take will be too far, so you can't really move at all -?

which means that to move from 1 to 0.99999..., you have to stay at 1.?

Which means they must be the same thing!

Source = From link on page 8

AKA if you dont want to click on page 8

Here: http://mathforum.org/library/drmath/view/55746.html

[John Veteran]

it's not infinite...

[John Veteran]

Again i would like to quote my dr math friend Dr. Ian

This is a letter from 2 girls with this very problem of understanding, please read it.. It is generally excepted that

1 = .999 [repeating]

Date: 03/21/2001 at 16:22:11

From: Doctor Ian

Subject: Re: .999999..... I still don't get it

Hi Emily and Jenny,

There's no doubt that this equality is one of the weirder things in

mathematics, and it _is_ intuitive to think: No matter how many 9's

you add, you'll never get all the way to 1.

But that's how it seems if you think about moving _toward_ 1.? What if

you think about moving _away_ from 1??

That is, if you start at 1, and try to move away from 1 and toward

0.99999..., how far do you have to go to get to 0.99999... ?? Any step

you try to take will be too far, so you can't really move at all -?

which means that to move from 1 to 0.99999..., you have to stay at 1.?

Which means they must be the same thing!

Source = From link on page 8

AKA if you dont want to click on page 8

Here: http://mathforum.org/library/drmath/view/55746.html

ummm... no.

you can't "move" away from one with an infinitely small number. you can only "move" with a real number. 1-0.999... yields an infinitely small number, one that you can't count with.

[ericnkatz]

it's not infinite...

Ok what is 1 divided by 3?

Are you telling me it is .33333333333333333333334 if so you are rounding...

Because it is .33333333333333333333333333333333333333.... ............33333333333 etc.. etc.. [infinite]

If you multiply it by 2 [finite]

You get

.6666666666666666666666666666666..... ...........6666666666666 etc.. etc... [infinite]

How does it work you ask,

Multiplying a finite number by an infinite number?

Take this for an example

2 (1/3) = 2/3

2 divided by 3 =

.6666666666666666666.... 666666666666666666 Etc.. etc.. [infinite]

So what you said earlier gameguy is incorrect

[Captain Crunch]

Maths? *Turns into dumb blonde mode*

[ericnkatz]

Again i would like to quote my dr math friend Dr. Ian

This is a letter from 2 girls with this very problem of understanding, please read it.. It is generally excepted that

1 = .999 [repeating]

Date: 03/21/2001 at 16:22:11

From: Doctor Ian

Subject: Re: .999999..... I still don't get it

Hi Emily and Jenny,

There's no doubt that this equality is one of the weirder things in

mathematics, and it _is_ intuitive to think: No matter how many 9's

you add, you'll never get all the way to 1.

But that's how it seems if you think about moving _toward_ 1.? What if

you think about moving _away_ from 1??

That is, if you start at 1, and try to move away from 1 and toward

0.99999..., how far do you have to go to get to 0.99999... ?? Any step

you try to take will be too far, so you can't really move at all -?

which means that to move from 1 to 0.99999..., you have to stay at 1.?

Which means they must be the same thing!

Source = From link on page 8

AKA if you dont want to click on page 8

Here: http://mathforum.org/library/drmath/view/55746.html

ummm... no.

you can't "move" away from one with an infinitely small number. you can only "move" with a real number. 1-0.999... yields an infinitely small number, one that you can't count with.

Ok now...

Click the link..

It shows examples to help clearify the confused and misunderstanding people.

http://mathforum.org/library/drmath/view/55746.html

http://mathforum.org/library/drmath/view/55746.html

http://mathforum.org/library/drmath/view/55746.html

http://mathforum.org/library/drmath/view/55746.html

Click it and READ

If you still think I am wrong after actually reading the article i have nothing more to say to you =\

[John Veteran]

Ok what is 1 divided by 3?

Are you telling me it is .33333333333333333333334 if so you are rounding...

Because it is .33333333333333333333333333333333333333.... ............33333333333 etc.. etc.. [infinite]

If you multiply it by 2 [finite]

You get

.6666666666666666666666666666666..... ...........6666666666666 etc.. etc... [infinite]

How does it work you ask,

Multiplying a finite number by an infinite number?

Take this for an example

2 (1/3) = 2/3

2 divided by 3 =

.6666666666666666666.... 666666666666666666 Etc.. etc.. [infinite]

So what you said earlier gameguy is incorrect

no, i'm not telling you that, i was responding to ike, i meant that the calculator thinks of the result as finite. a CPU can't fathom an infinite number.

[John Veteran]

That is, if you start at 1, and try to move away from 1 and toward

0.99999..., how far do you have to go to get to 0.99999... ??Any step

you try to take will be too far, so you can't really move at all>

this only validates my claim that you can only count with real numbers. you can't move away from 1 with a real number, you'll just get a terminating decimal, which i think we all agree on, that this is NOT 1.

stop thinking "real" and think of a number an infinitely small distance from zero. it doesn't "exist" but it's the difference between 0.999... and 1.

[ericnkatz]

Ok what is 1 divided by 3?

Are you telling me it is .33333333333333333333334 if so you are rounding...

Because it is .33333333333333333333333333333333333333....  ............33333333333 etc.. etc.. [infinite]

If you multiply it by 2  [finite]

You get

.6666666666666666666666666666666..... ...........6666666666666 etc.. etc... [infinite]

How does it work you ask,

Multiplying a finite number by an infinite number?

Take this  for an example

2 (1/3) = 2/3

2 divided by 3 =

.6666666666666666666.... 666666666666666666 Etc.. etc.. [infinite]

So what you said earlier gameguy is incorrect

no, i'm not telling you that, i was responding to ike, i meant that the calculator thinks of the result as finite. a CPU can't fathom an infinite number.

I know,

Ike's example is alittle off target, but it does feed the point

You just need to do it by hand,

not with a calculator,

Cause in fact calculators are a bad thing to depend on in this situation.

But do it by hand and what your saying only applied to the calculator,

1 = .9999 [repeating]

without a calculator..

Just read the link i have posted multiple times

http://mathforum.org/library/drmath/view/55746.html

[CtotheJ]

I'm a man of few words. I really don't care to argue this with a bunch of people on the internet, because that would be a waste of my time of which I have very little. So, I will not respond to any follow-up unless someone kindly and sencearly requests clarification.

Everyone who posted that .99999 repeating was NOT equal to 1 is correct. The people who claimed that it was equal to one forgot one thing: 1/3 is NOT equal to .33333 repeating.

1/3 can not be expressed exactly in base 10, just as pi can not be expressed exactly in base 10, just as e can not be expressed exactly in base 10. When people pull their third grade 'math skillz' showing

1/3 = .3333 .'. 3/3 = .9999

they messed up where they said that 1/3 was equal to .3333 repeating. The reason they end up with a number less then one at the end is because those little tiny rounding errors add up.

I wonder how many people in this thread tried to pull that scam from Office Space on their companies? ;)

Dazzla has said one smart thing on this thread: You can not do this with a calculator. That is because when your calculator converts from a fraction to decemal in base 10, it rounds. A calculator will incorrectly tell you that 1 / 3 = .33333 repeating. In fact, it is approx. equal to it. But then again, your calculator will also incorrectly tell you that pi = 3.14159265.

[ericnkatz]

That is, if you start at 1, and try to move away from 1 and toward

0.99999..., how far do you have to go to get to 0.99999... ??Any step

you try to take will be too far, so you can't really move at all>

this only validates my claim that you can only count with real numbers. you can't move away from 1 with a real number, you'll just get a terminating decimal, which i think we all agree on, that this is NOT 1.

So your saying there is

.00000000000000000000000000000000000..............0000000000000000000000 [repeating infintely] [then] 1

When in fact no such number is possible because the number of 0 is infinite you will never reach the 1 at the end

Because , Infinity has no end,

Since you never reach the 1 at the end you are essential just adding 0 to .99999999 [repeating] to = 1

So your saying there is 0 difference between the 2 numbers prooving whos point?

Well my point.. :DD

[ike]

i was originally responding to samoa's post with my calculator thing of 1/3 being multiplied by 10, i was trying to show how you can multiply a repeating decimal by 10. gameguy claimed that my calculator was rounding, which i then explained why i felt it was not because it was maintaining internally that the decimal was repeating.

[John Veteran]

So your saying there is

.00000000000000000000000000000000000..............0000000000000000000000 [repeating infintely] [then] 1

When in fact no such number is possible because the number of 0 is infinite you will never reach the 1 at the end

Because , Infinity has no end,

Since you never reach the 1 at the end you are essential just adding 0 to .99999999 [repeating] to = 1

So your saying there is 0 difference between the 2 numbers prooving whos point?

Well my point.. :D

no, that's now what i'm saying. i agree with you that no digit can exist after infinity, because that's the nature of infinity.

you're still using real numbers.

[John Veteran]

i was originally responding to samoa's post with my calculator thing of 1/3 being multiplied by 10, i was trying to show how you can multiply a repeating decimal by 10. gameguy claimed that my calculator was rounding, which i then explained why i felt it was not because it was maintaining internally that the decimal was repeating.

any calculator/computer/device will terminate the decimal. computers can't understand the concept of infinity.

[ericnkatz]

So your saying there is

.00000000000000000000000000000000000..............0000000000000000000000 [repeating infintely] [then] 1

When in fact no such number is possible because the number of 0 is infinite you will never reach the 1 at the end

Because , Infinity has no end,

Since you never reach the 1 at the end you are essential just adding 0 to .99999999 [repeating] to = 1

So your saying there is 0 difference between the 2 numbers prooving whos point?

Well my point..  :D

no, that's now what i'm saying. i agree with you that no digit can exist after infinity, because that's the nature of infinity.

you're still using real numbers.

If there is nothing in between them,

Are they not equal? :ninja:

If there is nothing between 2 numbers then they must be the same, regardless of real numbers, imaginary numbers etc.. etc..

[John Veteran]

If there is nothing in between them,

Are they not equal? :ninja:

If there is nothing between 2 numbers then they must be the same, regardless of real numbers, imaginary numbers etc.. etc..

there is no real number between them. there is an infinitely small number between them. this number can't be counted.

edit: extra quotes removed.

[El Bourricot]

aleph * aleph = aleph

aleph + aleph = aleph

etc.

so yes

.9 recurring means the nos go on for inifity

line them up:

10x 9.9999999999...

-x 0.9999999999...

=

9x 9.0000000000...

now if you round up either of 10x or x, you'll get 9x = 0.000...01. If you take it that there is an infinite number of 9s, it's different.

[John Veteran]

aleph * aleph = aleph

so yes

:huh: what's aleph?

[ike]

any calculator/computer/device will terminate the decimal. computers can't understand the concept of infinity.

i'm not sure you're getting my concept i was trying to prove. the concept i was attempting to prove is that it's possible to multiply a repeating decimal by an integer such as 10.

[Mixophrenia]

I think Proxy and Dazzla know what they are doing

So...

Yes :p

[John Veteran]

i'm not sure you're getting my concept i was trying to prove. the concept i was attempting to prove is that it's possible to multiply a repeating decimal by an integer such as 10.

i understand your concept, but i'm saying you can't multiply 10 times a repeating decimal... not without losing SOME accuracy. (i'm referring to a NONREAL number, so you won't be able to see a numerical difference between the number and 10 * the number)

[El Bourricot]

aleph * aleph = aleph

so yes

:huh: what's aleph?

The symbol aleph (hebrew letter) with a subscript 0, 1, 2, etc., invented by Cantor, denotes the order or the different level of infinity.

[ericnkatz]

aleph * aleph = aleph

so yes

:huh: what's aleph?

The symbol aleph (hebrew letter) with a subscript 0, 1, 2, etc., invented by Cantor, denotes the order or the different level of infinity.

:D

You speak hebrew, im learning it

:D

But thats off topic, im just getting down to the point that this is excepted by every mathamatic authority i know, in fact 1 out of my 2 friends who disagreed with me originally has come to my side.

[El Bourricot]

for those who need to rework their concepts of infinity

http://www.hypermaths.org/quadibloc/math/infint.htm

not very good... but enough.

edit - just noticed there have been 10 pages of links posted... :blush: my fault for being so lazy and not looking

Edited October 2, 2003 by cofrog

[John Veteran]

i'm curious. who here has taken a calculus or pre-calculus class?