once some people here have learned to take the limits of x approaches to infinite for various functions, they will understand better...

for now, look up on L'Hopital's rule

also i forgot what is the question which this thread started upon
lol

it was does .99 = 1.. just by looking at the question should give the answer. :/ This thread is just a bunch of overanalysis.

22/7 is approximated fraction, 1/3 is not
 

if you ever go and calculate it by hand or calculator you'd find that 22/7 is in no way cloase to 3.14159265359.......
though 1/3 is very accurately 0.3 repeating.
I agree that 0.9 repeating is not so true for real life because you will never use that many numbers, but since we are talking about algebra here, I'd have to say 0.9 repeating=1 is algebratically true! :)

Sigh. .9~ does equal one.
 

If you don't believe this last proof, then you have
1. Have disproven the value of the natural Logarithm "e"
http://www.jimloy.com/algebra/series.htm

2. Have disproven the value of PI, as defined by the infinite sum of a geometric sequence http://www.jimloy.com/algebra/seriez.htm

http://www.richland.cc.il.us/james/l...geometric.html

As you can see, the infinite sum of a geometric sequence is equal to:
S= a1 / (1-r )

It's proof is shown here:
http://www.math.unl.edu/~gnorgard/calcres/gseries.html (just click "answer")

That such a thing exists.

Where S is the series. (an infinite sum of a geometric sequence)

Thus, we fill in the values. .99999~ is a series, moddled by .9+.09+.009+.0009 ... (9*10^-n)

a1 == .9 (the first value of the sequence)
r == .1 (a(k+1)/a(k) where k is a positive integer)

S = .9/(1-.1) == .9/.9 == 1

Thus, .9~ (the infinite geometric series, .9+.09+.009+.0009 ... (9*10^-n)) is equivalent to one.

Remember, both PI and E are defined by an infinite series/infinite geometric sequence. Thus, you disagree with this, you disagree that PI == 3.141592 ...

Again, for those who do not believe .3~ is equal to 1/3. The infinite sum of the sequence .3 + .03 + .003 ... (3*10^-n) is equal to

al == .3
r == .1

.333~ = .3/(1-.1) == .3/.9 == 1/3

I'm in calculus, and I still don't believe it.. I don't think any formula or equation could convine me either... it's just one of those things...

....called irrationality. The point of mathematics and science and logic is to overcome those things which we believe to be true to find what can be shown to be true. Without a doubt, this is one of those cases, except perhaps if you apply Godel's Incompleteness theorem, but I don't think that is necessary at this point.

*shrugs and continues studying permutations*

Well, if you want to make that analogy, you have to make it completely. You aren't taking off an entire grape. Go down to a singular cell, then go down to a single molecule of it. Now go down to a single atom of that molecule. Within that molecule you have subatomic particles, choose one, if it's not an electron you go down another level to strings that make up subatomic particles, if you do go to the electron its a string already. Now take an infinitely small amount of the energy that makes up a string out. The string is still a string, because not all strings have exactly the same amount of energy, its the string equivalent of a wavelength that determines its properties anyways, so your real life example was just shut out by String Theory. :P

James, I quite agree with you. The reference you made to me earlier in that post was referring to me before I took Calculus. While I agree that one cannot understand the concepts necessary to understand any truths of this without understanding the concepts one learns in Calculus, I don't think they shouldn't be a part of the discussion. They just won't be right, that's all ;).

Jason425, if you have seen L'Hopital's Rule, (lim f(x)/g(x) = lim f'(x)/g'(x),)you will agree with me when I tell you that 1 (or any constant) divided by infiniti is equal to 0.
1 - .9~ = 1/(infiniti)
Deny that! :evilking:

No, I haven't seen it.. but we're just getting into limits.. so i'm sure soon i'll be corrupted into believing you two ;)