If .999… equals 1, then surely there is another number .999…8 that equals .999…
Does anyone see a problem with this?
Ah, but how would you represent such a number? When would you put the 8 on the end? There’s alway somewhere else to go. There is no way to represent an infinitely long string of 9’s with an 8 on the end mathematically. But there is a way to represent .9999… mathematically. And you can’t say that the limit of this function can just as easily equal the .999…8; this limit shows a direction of growth towards 1.
trivial much?
ya every number would then equal every other numeber… which is why .999[bar] does not equal 1
Wonderer, you skipped Anthem’s response, and my response to LJ before that. There is a serious problem with rigorously defining a number that is an infinite string of nines followed by an eight; the string both does and doesn’t have an end, which is absurd.
i would like to make it clear i am not associated with lady jane… i do not wish to be involved in her posts and i wish she would stop posting the same thing over and over in mine…
when i replied to faust i was using his interpretation to justify something to him, as many people are arguing against me from different points all at once, my posts may seem irradic…
generally i try not to contradict myself
LJ can speak for hersef… no association…
which response from anthem?
Sorry, I meant Anthem’s response to Faust’s musing, “If .999… equals 1, then surely there is another number .999…8 that equals .999…”
Another thought I just had:
Even if ‘.999…8’ is a possible number, it doesn’t compare to ‘.999…’, but to ‘.999…9’. These are very different numbers! One has a last decimal place, the other doesn’t. One is traditionally infinite, one isn’t. One can truly be said to equal 1, the other can not. And in fact, it’s quite simple to determine the sifference between .999…8 and .999…9: .000…1.
Carleas and anthem - I realise the problem with my counterexample. But it is equally ludicrous to suppose that any number is equivalent to a different number. The very definition of “number” would have to be changed. Until this is done, .999… is never going to equal one.
Carleas - .999… is either a number or a string of numbers - it is not both. Even pi must be ended in order to be used as a number. Nothing infinite is functionally a number at all.
The fact is that we must, somewhere along the line, “fill in” some number for this "proof’ to work. Every number is subject to the notion of succession. Or it is not a number.
geeeee
it has already been shown you have no non-circular definition of number thus you dont even know what a number is
talk about closed mind in the face of evidence
But .999… isn’t its own number, it’s 1 
.999999999999999999999999999999999 is it’s own number. So is .99999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999, but .999… isn’t really a number or even a string of numbers; it’s an infinite series that converges to 1, which is a number.
You can also think of it in terms of accuracy and precision, since you brought it up, Faust. Let’s say you measure some length to be .99998357 m, but it’s only accurate to the milimeter. You would round this number up to 1 meter. That doesn’t really have much to do with convergence, but it does show that .999… still becomes 1 in practice.
but colin leslie dean has proven .99999=/1
so now you have contradictory math proofs showing as dean says maths ends in meaninglessness
oh
and
no comment about you not even knowing what numbers are except in circular -thus illogical- definitions
No you haven’t. Your ‘proof’ is absolute nonsense and doesn’t follow the rules of mathematics. You don’t think 1/3 * 1/3 = 1/9, for God’s sake.
No comment on the numbers being circular? I did in another thread you made. Reported again.
sci logic says deans proof is legal
Reported for a repost.
Oh, by the way, I didn’t put the summation in my limits.
I should have written things like:
lim (n–>infinity) sum (m = 1 -->n) 9/10^m
It just gets confusing when you’re trying to type it out instead of write the nice compact little symbols.
Faust, I’ve been a little sloppy in my vocabulary, let me try again:
.999… and 1 are the same value, they are just different ways to refer to it. Just like .25 and 1/4 are the same value, 1 and .999… are two symbolic representations of the same value. In math, they are interchangable.
.999… is an infinite string of digits. One number, many digits of the number. Math is so formal sometimes.
i was confused earlier about whom the pragmatist is…
at first i thought it was me for saying that .999[bar] can never equal one in practice due to our finite nature and our perception of time, but is in fact the opposite because .999[bar] assumes the practicality of limits when you theorize about them…
this whole thread is about the impracticality of limits… when we try to represent 1/3 as 1 number, we then lose precision when we plug that into a calculator… because the 9’s can never finish calculating… so we assume that if it somehow did finish, (lets say god finished it for us), we assumeit would equal it’s limit… what we want it to equal…(1/3).
i hereby assert the notion that infinity can cancel out infinity is false.
in the sense that given we have an infinite number of 9’s we can write, the idea that those 9’s can be written would not only define infinity (the undefinable) as well as prove that we do not exist… and also the assertion that there are infinite 9’s to be written is just as unfounded as the notion that they can be written.
now how the heck would this prove we don’t exist you may ask?
well, if there exists an infinite number of 9’s that can be written, and someone writes those 9’s . the fact that we exist and we are not entirely composed 9’s would mean that there is more room in the universe for more 9’s, making those “infinite 9’s” not so infinite. so even if there are infinite 9’s to be written, they cannot be.
so given this paradox of infinity canceling out another infinity is impossible… or else we don’t exist…
now that i have your attention…
what happens when you multiply .9999 by 10? you get 9.9990
not 9.999 because it is less precise than its original, not 9.9999 because it is just wrong.
you see it is a simple loss of precision when you multiply… the complex and twisted ideas of infinity that apply to our number system simply do not conform to it. they cannot by nature… that is the reason why you need .333[bar], and saying that .999[bar] equals 1 via limit… well thats is just a waste of time and pointless mathematics when you have a perfectly good prime number instead…
i have already asked someone to show me how .999[bar] is created…
how does mathematics produce that specific “number/representation”?
if 1/3 = .333[bar] = x
then 3x = 1
there are no 2 ways around this… by saying .333[bar] x 3 = .999[bar] = you are simply saying screw precision as in practicality we don’t need infinite precision…
this makes you the pragmatist and not i 
p.s pragmatism is wrong IMO 
not quite… .333[bar] as it stands is not a real number no, but when we use it we just type in a bunch of 3’s and then use our brains to fill in the loss of precision from an actual third.
by using .99999999 instead of 1 our brains can similarly compensate for the loss of precision but that would be the insane mans way of doing things… we have a perfectly good number.
p.s .999[bar] equals nothing relative to quantity because you cannot define it
though i can barley remember the symbols, some people are not privy to such luxury. when i explain it then i can question myself, not debatable symbols.