Argued with a couple people about this today. Basically the idea is that in a real number system 0.9999999 with 9 extending for infinity, is equal to 1. They are the same number.
I understand the mathematical concept with real numbers, but I prefer the infinitesimal number system when it comes to this. I feel it is far more logical to assume that 0.999... never reaches 1, it just infinitely gets closer and closer, but never becomes 1. This I think is far more representative of physical world realities.
I like the geometric series example when it comes to this. Basically
0.999...= 9/10 + (9/10)^2 + (9/10)^3 + .... = 9(1/10) / (1-(1/10)) = 1.
So 0.999... converges to 1. For all intents and purposes, any use of the real number system would use this, and would not treat both numbers as different.
Jun-04-2012 06:27
LAdazeNYnights
Crossing Swords
Registered: Nov 2009
Location: Los Angeles, CA
.333 + .666 = .999
1/3 + 2/3 = 3/3 = 1
you can't explain that.
science.
Jun-04-2012 06:58
Taipan
tranceaddict
Registered: Jan 2011
Location: New York
quote:
Originally posted by LAdazeNYnights
.333 + .666 = .999
1/3 + 2/3 = 3/3 = 1
you can't explain that.
science.
/thread.
Jun-04-2012 07:18
Joss Weatherby
young & cold
Registered: May 2008
Location: The Ruins of Rome | Cascadia
