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