0.999 exactly equal to 1?

ERM ... can anyone find a proof that 1=1 and does not also =.999
in other words 1=1 and !1=.999 ?

 

Firstly, there is a decimal representation of 1, it's 1, seems trivial, by technically it's a decimal.

It's not because of rounding, though for purposes of basic arithmetic rounding is acceptable.

You seem to have gotten halfway there, it is due to there being an infinite number of places, but you do not have to stop anyplace. The numerical difference between .999 repeating and 1 is of course important, but it's not simply a matter of the difference being very small. The difference is in fact infinitly small. It is for this reason that in an arithmetical sense 1=.999 repeating. No rounding is involved here, neither is the inability to deal with the infinite.

That is so seriously retarded that I could not help but reply to it. You don't push the same buttons to type "1+1" as you to do type "2". So are you telling me that 1+1 does not equal 2?


Edit: Oooh here is another way I though of to do it.

10-.9=.1
10-.99=.01
10-.999=.001

We see that for every nine added to the equation on the right side of the decimal we add another 0 between the decimal and the 1 in the result.

So if we do this
10-.999 repeating
we can never reach the 1, there are an infinite number of zeros before it. So while the 1 is there in some kind of theoretical sense, there is another sense in which it is never there. It is the final number in an infinite sequence and can therefore never exist since if it did the sequence would not be infinite.

 

I can't agree more.

 

.999 is .999, and 1 is 1. 1 is .001 more than .999.

 

Of course no-one is telling you that
the statement 1=.999recurring is precisely that
so what we are telling you is that .999r + .999r = 2
as well as 1+1=2
read my post prior to this !!!! it explains the proof - now you are not going to argue against the whole of the mathematical world are you including its most eminent professors and the leading mathematical lights of our time?

1/3 = .333 agreed?
so 2/3 = .666 yes?
and 3/3 is .999 huh?

ok now go to google calc and type in
.99999999999 + .99999999999
and it will tell you the answer is 2
here it is
Google calc .999 + .999 = 2

you might like to try this as well

1 + .999999999999999 = 2

and

[size=+1]2 - .99999999999 = 1[/size]


Unless you can provide proof of the statement:

1=1 and 1 is not (!)=.999999999999
then you have to accept that 1=.999.
in light of a lack of evidence against this proposition - you are stumped and have to rely on faith that
1=1 and !1=.999

I tell you that evidence is either not there or terribly difficult to find
I have shown that 1=1 and 1=.999
you must show 1=1 and !1=.999
in mathematical terms

 

you are all extremely retarded. why are u using all of these tschnological terms to try and prove that .999 and 1 is the same number. .999 is a dofferent number than 1. everyone get out your calculators and type .999 plus .001 and you will get the number 1. 1 is .001 more than .999. thats like saying .998 is the same as.999. geez.

 

why the hell did i make this thread haha, all people do is argue about a stupid question i stopped caring about 10 minutes after i made it.

 

i think people stop caring the minute after they post.. but yah it is pretty pointless and just proves how stupid everyone really is.

 

Actually the reason is
People care about this stuff in the same way they care that people
should accept the truth - those that argue against the proof havent accepted that the world is not EXACTLY as they thought it was
and so fight it .
The ones who accept the proof are so amazed by it that its that simple - that it kind of is like a new toy ! And I like messin people up with the truth


SO for all the retards out there

the point is this

.999 RECURRING means 0.9 with an infinite number of 9's following that
now if you shorten that to something like .999999999999
for the sake of convenience
otherwise you would fill the entire internet with a row of 9's

then the point is that a proper scientific calculator will tell you that
.999999999999r (ok retards the r stands for recurring)
plus .999999999999r
equals 2
and this is because one third of one = .33333r decimal
so two thirds of 0ne is equal to .666666r
and three thirds of one (which should equal one because 3 divided by 3 = 1)
in fact does equal 1 but also equals .99999999r
so 1/3 = .33333r
2/3 = .66666r
and 3/3 = 1 and also equals .99999r

how can this be - now the proof is there
go to google and type this in
.999999999999 + .999999999999
it will know if you put in twelve 9's after the decimal point you mean recurring
now according to google and all other scientific calculators
.999999999999 + .999999999999 = 2
and .999999999999 - 1 = 1

If you want to say this isnt the case you have to show a mathematical proof that
1=1 and does not also equal .999r
in such a way that I cannot argue that
3/3 =1 and also = .999r
so anyone who wants to try can impress us all with the proof that
(! means not)
1=1 and !1=.999r

 

While the lim(.9999...)does equal 1 this does not mean that 0.999... equals 1 because no matter how many decimal places i go I can always find a number that fits between that number and 1. Therefore they can't be equal. In fact there are an infinite numbers that will fit.

The problem is that the finite decimal system can only approximate the infinite but it is the best we can do.

Those using the arguement that 1/3=0.333 and 2/3 =0.666 are forgetting that these are not exact in fact 2/3 is closer to 0.667.

As far as using calculators (or google) to prove a point once again these are only finite tools that approximate reality and only do what they are program to do. Thus they cannot be used to prove anything.

 

ahhhh thats what i used to think...

but remember a recurring number is the only way we can represent some numbers

see my later posts, the fractional proofs offered later by other people are a wonderful way to see these numbers.

 

man this thread has just mind fucked me head man ..........if 9=1 then what does 91 equal ..............man ime outta here

 

I dont know how anyone can see .999 or any number of 9's after that as 1. Unless your on drugs, then that might make sence.

 

http://en.wikipedia.org/wiki/0.999...

 

that site seems to overcomplicate it. yeesh

 

the simplest way to understand it is this...

the decimal system can only represent numbers such as 1/3, 2/3 as recurring decimals

eg

1/3 of a cake is always 1/3 of a cake, decimally 1/3 of a cake is 0.3 recurring, no one has told the slice of cake that it is a number getting closer to 1/3 as 0.3333333.... would suggest.

 

Wikipedia does not mean its true. saying .999 is equal to 1 is no different than saying 2 is equal to 4.

.99 is a different number than 1, regardless of how close it is to 1 they are not the same number even if there are a million 0's, it is still not quite 1. I cannot be convinced otherwise. These "proofs" do not do it for me as they are still different numbers at the end of the zero rainbow.

 

Well who are we going to believe - the proffessors of mathematics who in wikipedia explain that
numbes are not a unique identifier to a literal quantity, or you ?

Just because you dont understand what wikipedia is saying doesnt make it false !

now the siple explanation is that numbers need not represent one value
otherwise explain this
(... = recurring into infinity)
1/3 = .33333...
2/3 = .66666...
3/3 = .99999...
AND 3/3 = 1

how can that be unless its true ????? numbers may express more than one value
therefore 2.999.... = 3
and also 2.9999...

One way to see it is like bandwidth where a number expresses itself and its immediate relation
so 3=3 and 3=2.999... and 3=3.111...
that is the truth of the matter that is what wikipedia is explaining - I have visited several maths forums and had it explained in great detail to me
the simplest way to understand it is this...

similarly no-one told the decimal it could not express itself as a fraction
1/10 = .1
to use the analogy of the cace you would have to cut it with an infinitely thin blade edge or you would not have precise cutting

 

You're wrong. "Let X=0.999" and then, "which means X=1". 1 and 0.999 are two mutually exclusive numbers. X cannot equal two different numbers in the same equation, therefore the equation is flawed hence invalid.

 

read through the previous posts