>>39
Read what I typed. You are just talking in circles. >>41
That sucked. I said divide, not convert division into other operations.
Name:
Anonymous2007-01-02 17:27
>>43 which referenced >>39 (correction to >>44 above)
Read what I typed. You are just talking in circles.
Name:
Anonymous2007-01-02 18:21
>>41
Also, that manoeuvre doesn't even work with most cases: 1/1, 2/2, 4/4, etc. unless you pull another fast one and convert them to 3/3 first. And, you trade one problem for another, relying upon another infinite set version of a fraction (1/3 = .333..., a representation that I poo-poo on) upon which you attempt to perfom an arithmetic operation upon (multiply by 3), which I also poo-poo on.
But that just makes more points to argue about. All I wanted was in that post was division performed, eg 4 divided by 4.
Name:
Anonymous2007-01-02 18:23
>>45
Proving that 0.999... = 1 is simple, since 0.999... = lim n->+inf of the sum from i=1 to n of (0.9 * 10^(-i)), which is equal to 1. Hence 1/1 = 2/2 = 4/4 = 1 = 0.999...
Name:
Anonymous2007-01-02 18:27
That's just repeating what you said. You are talking about your proofs when something else was asked to be demonstrated.
Name:
Anonymous2007-01-02 18:51
Sure, you might be able to prove that .999... = 1, but how do you prove that .999 equals the experience that a black man living in America must go through?
>>52
Listen very carefully: I proved that 0.999... = 1. Hence, 1/1 = 2/2 = 4/4 = 1 (you agree with this, right?) which, in turn, = 0.999...
Name:
Anonymous2007-01-03 2:35
>>53
Uh, that's not what I asked for. I didn't ask for a proof, I asked for a calculation.
Name:
Anonymous2007-01-03 2:37
specifically, using the operation division.
Name:
Anonymous2007-01-03 2:40
>>54
You don't have the slightest fucking clue what you're talking about. Calculations are components of proofs and, in math, proofs trump all. Disprove him or concede.
Name:
LordRiordan2007-01-03 12:10
If .9999... were = 1 then it would look like 1 instead of .9999
Name:
Anonymous2007-01-03 15:20
>>56
No U, I didn't ask for a proof in my much earlier post. You are talking around what I was asking for, as if you believe that I am talking about what you want to talk about. Read the thread. I'm not talking about 0.999.... = 1 and making proofs one way or the other, that's some other guy. I wanted a demonstration that 0.999... can actually arise from the operation of division in the first place, as in 4/4. I can only conclude that you don't understand, or can't do it and are ashamed to say it, or are too hung up on proving 0.999... = 1 in every damn reply regardless.
>>58
0.999... can arise from the operation of division because it is equal to 1, and 1 arises from the operation of division. If you still can't follow this, gb2/middleschool/.
Name:
Anonymous2007-01-04 1:53
you can get it by writing out the long division for 1 divided by 1, and purposely leaving a remainder, lolz.
0.999...
1|¯ 1.000
-0
10
-9
10
-9
10
Name:
Anonymous2007-01-04 3:45
>>58
If you understood that .999... = 1, you wouldn't be asking that question. Does 1/4 = .24999... | 4/4 = .999... make it any easier?
Name:
Anonymous2007-01-06 0:38
>>61
Yes, that's my point. You can only get it with fucking up a long division. 0.9999... is a fucked up way to represent 1. >>62
I ask the question to reveal the lack of appearance of 0.999... unless it is specially contrived. I know that if you defined 0.999... as a limit you get 1, but really so what?
if .999... was not the same as 1, a lot of shit wouldn't work. calculus depends on this being true, and i'm sure it goes even deeper than that. that's "so what".
>>64
Calculus doesn't give a shit about the representation 0.999... specifically. A number and the representation of the number are not the same thing. We define the representations the way we do by convention. (Yes, your convention is the accepted convention.) The way we define the underlying number concept is another thing. >>66
Again, tease apart the concept of number from the concept of the representation of a number. >>67
obvious unfunny troll
It is worth noting that many typical text books (and Mathworld for easy-to-find online source) define series and their related sums not quite the same way as other sources (see Wikipedia for easy-to-find online source). I don't want to argue about one way being "the truth" as there is nothing new to add to what has been argued already -- what I want to say is that it is no surprise that people argue over what is meant by 0.999... when there are these two different common descriptions of series and their sums. If you want to be more convincing in your argument, you need to keep in mind how many people may have been taught, and speak to that (next post):
Name:
Anonymous2007-01-08 16:29
Mathworld - Convergent:
Most commonly, it is used to describe a convergent sequence or convergent series, where it essentially means that the respective series or sequence approaches some limit (D'Angelo and West 2000, p. 259).
Mathword - Convergent Series:
A series is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, the infinite series is convergent if the sequence of partial sums is convergent.
Mathworld - Series:
A series is an infinite ordered set of terms combined together by the addition operator.
If the sequence of partial sums converges to a definite value, the series is said to converge.
The above definitions suggest that to converge means to approach a limiting value, and so that a series sum approaches a limiting value.
Wikipedia - Series (mathematics):
The sum of an infinite series is the limit of the sequence of partial sums.
This limit can have a finite value; if it does, the series is said to converge.
The above defintion states that to converge means to become equal to the limiting value, so that the series sum is that limiting value.
The Mathworld and Wikipedia definitions conflict in thier treatment of the infinite series. Mathworld treats the convergent series as a sum that is approaching the limit, while Wikipedia defines a sum of the convergent series as that limit. (Yes, elsewhere on Mathworld you may find definitions of real numbers that use the limit.)
People argue with you over 0.999... because they believe they see a series sum that approaches a limit, which may have been how they were taught about series sums. This idea is reinforced by their memory of learning long division, where they produce each digit successively from left to right, suggesting in their minds a successiveness to the parts rather than an immediate complete whole that has been partitioned into infinitely many parts.
Name:
Anonymous2007-01-09 2:48
Hm. After a few months of being away, I decided to come check out how /sci/ has been.