i was just wondering what peoples opions are abou this
it has plagued me for a while and i just dont know any more
does 1 equal .99999....(to infinity) or not

some one please give me advise as to what is the truth

Silly Mikey. No, it's off by .1 anyway you look at it.

If it were to equal 1, it would have to be 1, not 0.9(and however far you go)

Basic principle of whole numbers :P

Of course not...although kt has the right idea, not totally correct...0.9 (recurring) means it will never reach 1...it will get mighty close, but it will never reach it...because there is no definate amount of decimal places there...besides, 1 is a whole number...and no decimal number other than 1.0 can equal 1...

Yep, that sounds about right to me. It'll be off by a helluva lot less than 0.1 but never gets to one. Basic maths (well, pretty much)

I would like to counter the point that only 1.0 can equal 1. In terms of absolute value then -1.0 will also equal 1. If we are in terms of precision in data types then 1.324 would round down to 1 if it were converted into an integer. In terms of binary 00000001 would evaluate to 1, 0x01 would be equal to 1 in hexadecimal, both of which are basic languages that a computer can read. The truth of the matter is, we've made so many things that we can do with numbers since the beginning of time that things so simple don't work anymore.

Very true...but the topic wasnt on what 1 equals, but whether 1 = .99999etc...therefore, precision is the only factor that you mentioned that affects this discussion...the problem with precision however, is that it is an assumption...just because .99999999etc is incredibly close to 1, doesnt mean it is...and that is where precision falls short...precision is a convenience...if we had the space and time to use large and very accurate values, then we wouldnt use precision...so realistically it shouldnt count in this discussion either...

If we take all this into account, then .999999999999etc still does not equal 1...

It also makes logical sense that they are not equal...if they were, why would we have 2 symbol representations for the same number? Think about it...if an apple was the same as an orange, would we still call it an apple AND an orange? Of course not...the same applies here...

o_O apples and oranges? wtf xD

As long as it's a decimal, it will not equal the whole number 1. How's that? ^^,

NEVER QUESTION THE LOGIC!!!

I'LL QUESTION IT IF I FEEL LIKE IT, SO STFU! xD

Hmm.. well did any of you have THIS equation?

x = .999~
10x = 9.999~
10x - x = 9.999~ - .999~
Since both numbers have an equal number of decimal places (infinite), they cancel out.
9x = 9
x = 1
.999~ = 1

Get around that one..

DAMMIT MAN!!!

You know...I knew someone was going to eventually come along and prove that 1 does in fact equal .999etc...it seems like as soon as I try to prove something is wrong or right, I always seem to be wrong...always happens...

But good job Xen Si, you managed to get prove it so thats great...maybe you'll also be making regular appearances at AT as well now?

It does equal 1 now? Whaaaa?

x_x I hate math.

Technically yes...but logically no...Xen Si makes it equal, but if we weren't to use equations, then it wouldnt...either way, look at it how you want...

wtf. This is confusing x_x

JOE, YOU SUCK. xD

0.999... = 9/10 + 9/100 + 9/1000 + ...
so
(9/10)/(1-1/10) = 1.

or

1/3 = .333
so
1 = .999

but this is a Q that has no real answer.... people will always find a way to prvove and disprove the whole .999 ect... = 1, its a neverending topic....

I agree that .9999999~ is equal to one.

to me..... a decimal will never equal a whole number....

Technically... No. In some cases, yes.
It just depends on the issue that's trying to be resolved.
In math, yes, it can. There's simply no way around it.

yeah i guess.... but than agian... i suck at math........

heck.... i still dont get the whole multiplying negetive numbers = positive numbers thing.... its a mystery how I passed Math with a 97......

my head hurts.... im going to lay down...

Whaaa?

...can someone explain how it's equal without all this number mumbo-jumbo of equations? x_x I'm totally lost now.

the fact of the matter is, it doesnt equal 1 without equations...when I first posted my argument, I didnt think about the possibility of using equations to make 1 equal .999~, but obviously you can...

however, as we all know...a decimal, without the use of equations or any other means of manipulating the numbers, CANNOT equal a whole number...it just makes no logical sense...

it equals one because a small decial missing to make it one becomes insignifican after about 3 places look at it this way:


1.You got an apple nopw cut it into ten parts
and set one part aside .9
2.now take the piece you set aside and
cut it into ten parts and set
one of the small pieces aside .99
3. take the part you set aside cut it
into ten parts, put 9 of them back with
the rest of the apple set one aside .99
4. do it over and over agian till you cant cut it

you will not even get this far .999999999999

and in .999~ the 9's never stop coming

you see the part you keep cuttiiong gets so insignificantly small if you took a new apple and cut just that little piece out and asked some one is this and apple or .999999 apple's
what would they say?

like if you lost on skin cell its .9999999999~ of you but its still you!

have you taken a chemist classs?
in chemistry you learn about significan figures
there are many rules that are confusuing but in the end it ends up saying you really should have much more decimal places past the figure used before and to cut repeating decimals if you dont beleieve me go to a library and barrow a chem book the first few chapters will talk about this bu when u have a repaeting deciamal you have to round up look

.9999999
we are goign to round to
.0000009
so that # place becomes 10:
.999999
+
.0000010
=
.99999
+
.000010
=
.9999
+
.00010
=
.999
+
.0010
=
.99
+
.01
=
.9
+
.1
=
1

thats it really and if you dont believe me i have proof from blizzard in calculus using limits to explain mathmatically B.net had this problem lol
[url]http://www.blizzard.com/press/040401.shtml[\url]

Ok...dont double post...

I dont know if you read correctly, but as I said before, I definately acknowledge that the use of formulae and equations CAN prove that 1=0.9999~...

BUT, you have to understand that equations are there to make life simpler for us...but if you take raw numbers and compare them...then no they are not equal...As I've seen so far, only Joe has come up with an equation that doesnt use precision, which I already countered earlier...

As I said, precision is an ASSUMPTION...you are effectively assuming that because 9 one billionths is so small that it doesnt make a difference whether we include it or not...so we round off to the nearest whole number/decimal place...its for convenience...

But if in the case of trying to prove whether a number equals another number, precision cannot and should not be taken into account because it is merely an assumption...and this is why, although your method of removing "insignificant decimal values" is valid, it still assumes that decimal places are insignificant and shouldnt be take into account...

However, you can argue that Joe's equation is a very good example of how we can force 1 to equal .9999~, but then we get onto a new argument...whether manipulating numbers in order to make them equal is really a method of proving that they do in fact equal one another...

In my opinion, no...mainly because that if we didnt have equations, would 1 equal .9999~? Of course it wouldnt...because as raw numbers, no number can equal another number...because the numbers you use are merely symbols that reperesent specific and accurate values...if you have 1 thing, you have a whole thing...no missing pieces...but if you have .9999~ things...it is not whole...because there will be that piece that is so infinitely miniscule, that we interpret it as being negligable because our brains cannot compute infinity...but we assign the symbol ".99999~" to this value so that it is unique...so that we can define it seperately from every other value...

So, by this reasoning, if we had 2 of these symbols assigned to the same value, both would be meaningless, because neither is a clear definition of that value...so if 1 did in fact equal .99999~, then the value that those 2 unique symbols repersent would and could not be defined logically...

Hehe.. didn't mean to rain on everyone's picnic, but.. it's what I do :D. I can't take all the credit though.. there was a thread on this on another forum.. actually, it's everywhere apearently. I don't actually have an opinion on the answer because I don't care, but in the end someone said basically that factullly it is not equal to 1, and it can't truely be solved by an equation because 0.99~ is not a real number. Again, I have no opinion..

I suppose i'll change my opinion that i had in my last post...

We say that 0.333333~ is exactly 1/3. Multiplying this by three gives us 0.999999~ which appears to be 3/3=1. But whatever, it's a stupid topic now :)