Interesting question. Does 1.99999999999... = 2 [Archive]

BL!NKEY

18-08-2007, 05:11 PM

Is this because 1/3= 0.333 2/3= 0.666 3/3= 0.999 but 3/3= 1

ya that is one of the ways that makes me think it is true.

You can use .999999999... = 1 which is easier

1/9=.111111...
2/9=.222222...
3/9=.333333...
8/9=.888888...
9/9=.999999...
9/9=1

Ashley

18-08-2007, 05:16 PM

no, 1.999999 = 1.999999

Exactly, lol

VPSwow

18-08-2007, 05:20 PM

Yes.

My maths teacher proved it.

BL!NKEY

18-08-2007, 05:21 PM

no, 1.999999 = 1.999999

we are not talking about 1.999999999

Everyone can agree that that does not equal 2

the question is does 1.99999999... (repeating to infinity) equal 2

VPSwow

18-08-2007, 05:22 PM

0.9 recuring he means usually shown with a dot above the 9.

BL!NKEY

18-08-2007, 05:30 PM

0.9 recuring he means usually shown with a dot above the 9.

ya

here is a page with more reasons why it is equal
http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

Wootzeh

18-08-2007, 05:54 PM

Not a very good teacher is he if he doesn't know his their, there and they're s.
And no 1.999999 does not equal 2 because they're their own separate numbers, that's like saying pi is 3.142.

WarezKid

18-08-2007, 05:57 PM

it 1.9999 = 1.9999

Or i just dont ****** get it

Energizer

18-08-2007, 06:06 PM

no it doesn't..

Plank

18-08-2007, 06:10 PM

I would say it isn't because if your using an infinity number of recurring numbers, then it isn't going to reach 2?

No matter how many 9s you add, infinitely, it will NEVER equal one.

Additionally, all of your calculations have infinitely repeating decimals which you very kindly shortened up for us (which you can't do, because again, you can't represent the concept of infinity on paper or even in html). If you had stopped the numbers where you did, the numbers would have rounded and the calculation would indeed, equal 1.
Bottom line is, you will never EVER get 1/1 to equal .99999999... You people think you can hide behind elementary algebra to fool everyone, but in reality, you're only fooling yourselves. Infinity: The state or quality of being infinite, unlimited by space or time, without end, without beginning or end. Not even your silly blog can refute that.

Aflux

18-08-2007, 06:12 PM

No it doesn't.

FlyingJesus

18-08-2007, 06:17 PM

.9 recurring will always be infinitesimally smaller than 1, so no this can't be the case. Using fractions like that doesn't work, as it's an illogical method.

BL!NKEY

18-08-2007, 07:40 PM

it 1.9999 = 1.9999

Or i just dont ****** get it

That is correct but we are not talking about 1.99999

we are talking about 1.9999999999999999... (an infinite amount of 9's)

.9 recurring will always be infinitesimally smaller than 1, so no this can't be the case. Using fractions like that doesn't work, as it's an illogical method.

Why does 0.9999... = 1 ?
(http://mathforum.org/dr.math/faq/faq.0.9999.html)

Basically because there is no rational number small enough to fit between .9999... and 1. Therefore there is no difference making it the same number.

FlyingJesus

18-08-2007, 07:45 PM

So not having a rational number between two numbers makes them the same number? That's irrational itself.

BL!NKEY

18-08-2007, 07:47 PM

Maybe I explained that wrong. Maybe it was another word instead of rational number.

But the point was along the lines of if there is no number that can show the difference between .999... and 1 then they are the same number.

Wikipedia could explain it better

http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

Wootzeh

18-08-2007, 07:48 PM

That is correct but we are not talking about 1.99999

we are talking about 1.9999999999999999... (an infinite amount of 9's)

Why does 0.9999... = 1 ?
(http://mathforum.org/dr.math/faq/faq.0.9999.html)

Basically because there is no rational number small enough to fit between .9999... and 1. Therefore there is no difference making it the same number.
There is no number that can fit between .99999... and 1 because the next number has to be 1, it can't be anything else. My brain hurts :(

BL!NKEY

18-08-2007, 07:54 PM

There is no number that can fit between .99999... and 1 because the next number has to be 1, it can't be anything else. My brain hurts :(

Yeah so they are mathematically the same number.

Don't in-vision it as a long string of 9s (.9999999999999999999999999) with a 9 at the end because that is not an infinite amount.

FlyingJesus

18-08-2007, 08:14 PM

That's like saying there's nothing between A and B in our alphabet, therefore A = B

Wootzeh

18-08-2007, 08:17 PM

Time to go editting wiki pages. Nevermind I don't like Wiki, it edits it back straight away :(

Aflux

18-08-2007, 08:28 PM

Say if you have a loaf of bread, and a piece is missing - then it's not a full loaf of bread... it's something different?

BL!NKEY

18-08-2007, 08:56 PM

That's like saying there's nothing between A and B in our alphabet, therefore A = B

No what you are saying is that there is nothing between 1 and 2 so 1=2

But there is somehting between 1 and 2 which is 1 unit

There is no number between .999... and 1

Say if you have a loaf of bread, and a piece is missing - then it's not a full loaf of bread... it's something different?

But if you have a loaf of bread and you want to cut a piece off so that there is only .999... of the bread left you cannot cut off a small enough piece no matter how small a knife you have.

luke-p

18-08-2007, 08:59 PM

no, 1.999999 = 1.999999

Exactamundo

FlyingJesus

18-08-2007, 09:00 PM

There is no number between .999... and 1

There is because the recurrence is infinite - getting from infinity to anything has infinite possibilities.

Soil

18-08-2007, 09:01 PM

ya that is one of the ways that makes me think it is true.

You can use .999999999... = 1 which is easier

1/9=.111111...
2/9=.222222...
3/9=.333333...
8/9=.888888...
9/9=.999999...
9/9=1

No ... because you are dividing different numbers by 9 ... so you wont get 1. If you divide 9/9 then you wont get .99999999999 ... It doesnt always follow a pattern.

Axel

18-08-2007, 09:03 PM

No it's what it is, if it was 2 it'd just be 2.

Aflux

18-08-2007, 09:25 PM

What you are saying is that different things are the same as 1.9rec. is different to 2.

So a cat is different to a dog, therefore they are not the same?

Concentric2

18-08-2007, 10:09 PM

Just as the 0.999.. number is infinately big, the difference between it and 1 is infinately small, but being infinately small doesn't make it nothing, so there is still a difference.

BL!NKEY

18-08-2007, 10:15 PM

1/3 = .333...

2/3 = .666...

3/3 = .999...

I might not be the best at explaining it but wikipedia does a good job.

http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

Just as the 0.999.. number is infinately big, the difference between it and 1 is infinately small, but being infinately small doesn't make it nothing, so there is still a difference.

by infinitely small you are meaning .000...1 which is not a real limit number.

You cannot have reoccurring numbers to infinity and then another number at the end.

There is no difference

Concentric2

18-08-2007, 10:27 PM

You cannot have reoccurring numbers to infinity and then another number at the end.

I didn't say anything about it being recurring.

In any case, if a number is infinitely small you can't say what goes on the end of it because you're giving it an ending.

GhostFace-

18-08-2007, 10:28 PM

no its not 2 ;)

Shawnstra

18-08-2007, 11:41 PM

It never becomes 2, it just gets closer to 2 with every "9" added.

[DC]eption

19-08-2007, 12:08 AM

No it 2 is 2 and 1.9999 is 1.9999.

BL!NKEY

19-08-2007, 12:17 AM

It never becomes 2, it just gets closer to 2 with every "9" added.

But it never ends. There is no last digit.

there is no number that is in-between 2 and 1.999...

eption;3820888']No it 2 is 2 and 1.9999 is 1.9999.

we are not talking about 1.9999

this is 2 and 1.999... repeating forever

Azza

19-08-2007, 12:24 AM

1.9999999999 = 2 (1dp) :p
there is a theory, in my tiredness and bad maths thats proberly wrong though

Azza

19-08-2007, 12:25 AM

1.9999999999 = 2 (1dp) :p
there is a theory, in my tiredness and bad maths thats proberly wrong though
edit awww poop lag got to me and double posted, genius =]

Soil

19-08-2007, 07:29 AM

1/3 = .333...

2/3 = .666...

3/3 = .999...

I might not be the best at explaining it but wikipedia does a good job.

http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

by infinitely small you are meaning .000...1 which is not a real limit number.

You cannot have reoccurring numbers to infinity and then another number at the end.

There is no difference
My reply on page 2 kinda says what that is a load of bull.
Whoever wrote that explaination doesnt have a clue on maths.

1.99999 is 1.99999 NOT 2!

Virgin Mary

19-08-2007, 08:14 AM

Maths is annoying, but I'm pretty sure 1.999999999 is just 1.999999999, not 2. 3/3 is a fraction. I figure I'm wrong but oh well, just my $0.02.

Wootzeh

19-08-2007, 08:21 AM

But it never ends. There is no last digit.

there is no number that is in-between 2 and 1.999...

we are not talking about 1.9999

this is 2 and 1.999... repeating forever
STop telling people that you mean 1.99999... they know that they just don't put the dots >.>

Jambe

19-08-2007, 10:39 AM

When it is at 1.9999999 it doesnt jump to 2 1.999999 is an acctual number its not just 'Nearly 2' its just as important as any other number so no way is it 2..

BL!NKEY

19-08-2007, 06:37 PM

My reply on page 2 kinda says what that is a load of bull.
Whoever wrote that explaination doesnt have a clue on maths.

1.99999 is 1.99999 NOT 2!

Whoever wrote the explanation knows a lot about math and limits and infinity.

STop telling people that you mean 1.99999... they know that they just don't put the dots >.>

But they are two totally different problems.

If people are envisioning 1.999... as 1.99999999999999 with a lot of 9s.

That is not what it is. It is an infinite amount of 9s.

When it is at 1.9999999 it doesnt jump to 2 1.999999 is an acctual number its not just 'Nearly 2' its just as important as any other number so no way is it 2..

The truth is that 1.999... does equal 2.

I just posted this as a question so people would argue and eventually everyone would understand.

It turned out that no one here knows enough about math and infinities to understand.

Read what wikipedia says and you might understand. If you don't believe wikipedia then search google and see the hundreds of reasons why it is true.

http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

This is not a debate, it is cool mathematical thing that is kind of hard to realize at first.

Aflux

19-08-2007, 06:39 PM

BL!NKEY

19-08-2007, 06:43 PM

No, infinite is not a number, a number has to end somewhere - like everything else, it ends.

If it has no ending [which is the definition of infinite] then it's not a number, therefore it does not equal the same as a number, 2, because you're cross-classing things.

I am not going to argue with you because I am not some super smart mathematician.

I am just telling you that it is true and you can read about it on wikipedia and other sites.

This is not a debate forum.

We are not talking about the number infinity but a one with an infinite amount of nines after the decimal.

1.24999... with repeating 9s is 1.25

Wootzeh

19-08-2007, 06:56 PM

1.24999999... isnt 1.25 because it is 1.24999999... it keeps going, it doesn't go up -.-
It is not true.

hobo

19-08-2007, 07:05 PM

i think it is the same.
in a levels maths there was lots of things like this.

it's kind of like how anything to the power 0 should work out as 0, because you're multiplying the number by 0, but it's not, it's 1.
i cba to write out the rule for why, but you use it in pretty much ever second maths equation at a level.

& my teacher did tell us that when something worked out as x.999.... to put it up to the next number because they were the same thing.

N!ck

19-08-2007, 07:18 PM

BL!NKEY

19-08-2007, 07:22 PM

1.99 recurring and 2 are two completely different numbers. That does not mean that they are not equal to each other. Here is the way that I always prove this sort of thing to people.

1.99 recuring is 1.999999............. forever yes?

Call this 1.99 recurring x.

Multiply 1.99 recurring by 10, thus giving you 10x.

x = 1.99999999999999.........
10x = 19.9999999999999........

Now minus x away from 10x leaving behind 9x.

10x = 19.9999999999999........
- x = 1.99999999999999.......

= 9x = 18

If 9x = 18 then x = 2.

It's the same concept that that there is only 179.99 recurring degrees in a triangle, making it possible for you to have a two sided triangle ;).

But x also = 1.99 recurring :P.

Yeah that is a good example.

I still cannot envision the triangle with two sides though.

Maybe a link to a picture or something.

+rep

Soil

19-08-2007, 07:25 PM

1.99 recurring and 2 are two completely different numbers. That does not mean that they are not equal to each other. Here is the way that I always prove this sort of thing to people.

1.99 recuring is 1.999999............. forever yes?

Call this 1.99 recurring x.

Multiply 1.99 recurring by 10, thus giving you 10x.

x = 1.99999999999999.........
10x = 19.9999999999999........

Now minus x away from 10x leaving behind 9x.

10x = 19.9999999999999........
- x = 1.99999999999999.......

= 9x = 18

If 9x = 18 then x = 2.

But x also = 1.99 recurring :P.

It's the same concept that that there is only 179.99 recurring degrees in a triangle, making it possible for you to have a two sided triangle ;).

You can do that with a lot of things.

1.9999... and 2 are different numbers. 1.999 is NEARLY 2. NOT 2.

And dont believe everything you read on the net.

1.9999.. is a number.

N!ck

19-08-2007, 07:26 PM

I don't think it is possible to accurately draw one, because the sides are infinately close together.

Edit: @ Saurav - I never said 1.99 recurring was 2. I said it was equal to 2, which can be proven in the method i have shown.

Aflux

19-08-2007, 07:27 PM

I don't think it is possible to accurately draw one, because the sides are infinately close together.

It's impossible because a triangle needs to have 3 sides, otherwise it's just a line with a corner in it - an angle.

BL!NKEY

19-08-2007, 07:48 PM

You can do that with a lot of things.

1.9999... and 2 are different numbers. 1.999 is NEARLY 2. NOT 2.

And dont believe everything you read on the net.

1.9999.. is a number.

that is true that you shouldnt believe everything you see on the internet.

But this is on the internet with tons of reasons why and there are other pages on the internet talking about the same thing.

If one internet page said that 1.999... = 2 then I wouldn't believe it. But with the reasons and other pages you can trust it.

It's impossible because a triangle needs to have 3 sides, otherwise it's just a line with a corner in it - an angle.

Yeah I am still confused about this.

I cant find anything about it on google.

Concentric2

19-08-2007, 09:44 PM

I just posted this as a question so people would argue and eventually everyone would understand.

It turned out that no one here knows enough about math and infinities to understand.

Read what wikipedia says and you might understand. If you don't believe wikipedia then search google and see the hundreds of reasons why it is true.

http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

This is not a debate, it is cool mathematical thing that is kind of hard to realize at first.

I find it irritating that you say this not a debate, especially as you worded the title of the thread as a question, suggesting that you wanted to hear other people's views etc.

BL!NKEY

19-08-2007, 10:43 PM

I find it irritating that you say this not a debate, especially as you worded the title of the thread as a question, suggesting that you wanted to hear other people's views etc.

Yeah, I thought wording the title that way would lead to discussions and people talking about it. Then someone would show some ways why it is true and people would understand

It just turned out to be everyone telling me that it is wrong and no one would take the time to understand it.

So I posted the link showing why it is true but people still didn't believe it.

I wanted to hear other peoples views and watch them as they understand how it works.

Instead there are people claiming that it is totally wrong when there are pages written by people who are way better at math then anyone on this forum explaining how it is right.

If someone had a masters in mathematics and wanted to debate it then I would have no problem. I would actually enjoy watching what they say.

But the people who come on here and just go

1.9999999=1.9999999 not 2 duhhhh

annoy me because they are not even trying to understand it.

Virgin Mary

19-08-2007, 11:38 PM

Yeah, I thought wording the title that way would lead to discussions and people talking about it. Then someone would show some ways why it is true and people would understand

It just turned out to be everyone telling me that it is wrong and no one would take the time to understand it.

So I posted the link showing why it is true but people still didn't believe it.

I wanted to hear other peoples views and watch them as they understand how it works.

Instead there are people claiming that it is totally wrong when there are pages written by people who are way better at math then anyone on this forum explaining how it is right.

If someone had a masters in mathematics and wanted to debate it then I would have no problem. I would actually enjoy watching what they say.

But the people who come on here and just go

1.9999999=1.9999999 not 2 duhhhh

annoy me because they are not even trying to understand it.
Because it'll always be 0.1 off of 2.

ilove2spam

19-08-2007, 11:43 PM

NO WAI

BL!NKEY

20-08-2007, 12:11 AM

Because it'll always be 0.1 off of 2.

1.99 is not 0.1 off of 2

There is no number that can show the difference between 2 and 1.999...

Jinc

20-08-2007, 12:34 AM

1.99 recurring and 2 are two completely different numbers. That does not mean that they are not equal to each other. Here is the way that I always prove this sort of thing to people.

1.99 recuring is 1.999999............. forever yes?

Call this 1.99 recurring x.

Multiply 1.99 recurring by 10, thus giving you 10x.

x = 1.99999999999999.........
10x = 19.9999999999999........

Now minus x away from 10x leaving behind 9x.

10x = 19.9999999999999........
- x = 1.99999999999999.......

= 9x = 18

If 9x = 18 then x = 2.

But x also = 1.99 recurring :P.

It's the same concept that that there is only 179.99 recurring degrees in a triangle, making it possible for you to have a two sided triangle ;).

GCSE Maths ahoy!

Yes, it can be said that in this circumstance 1.999etc is equal to 2, but not the same number quite obviously.

If you were using the 1.999 in certain theorems, then it wouldn't be plausible to state that it is equal to 2.. but for most cases involving such numbers, the method shown by N!ck can be used.

Colin-Roberts

20-08-2007, 12:48 AM

technically it doesn't equal exactly 2 but in certain equations it would be ok to use it as 2.

Virgin Mary

20-08-2007, 01:19 AM

Just seems like another case of changing the facts to fit the logic.

RedStratocas

20-08-2007, 01:44 AM

Is this because 1/3= 0.333 2/3= 0.666 3/3= 0.999 but 3/3= 1

no it doesnt :/ anything divided by itself equals 1

and this question doesnt make any sense. because if it keeps going, how do you know what to compare it to? you can keep adding 9's to the end of 1.99 and it'll never turn into a 2.

BL!NKEY

20-08-2007, 01:54 AM

no it doesnt :/ anything divided by itself equals 1

and this question doesnt make any sense. because if it keeps going, how do you know what to compare it to? you can keep adding 9's to the end of 1.99 and it'll never turn into a 2.

ok but 2/3+1/3=3

we can agree on that

2/3=.666...
1/3=.333...
so 3/3=.999... or 1 which is the same thing.

also 1/9=.111...
2/9=.222...
8/9=.888...
9/9=.999...
and 9/9=1

along with the other reasons.

You do not keep adding nines. There is not a last nine. It is an infinite amount of nines.