How can this (math) be?

tw · 12-11-2006, 08:20 PM

I now see the subtle mistake in Shocker's 'cool math trick'.
Given S={1, 2, 4, 8 , 16...} and 2S={2, 4, 6, 8, 16, 32 ...},
then 2S + 1 = {1, 2, 4, 8, 16, 32 ...} IOW the infinite set called S and the infinite set called 2S has one less element than the infiinite set called 2S + 1. Yes they are all equal to infinity. But in each case, infinity has a different value. In the case of 2S + 1, the infinity also has one more element. Therefore we have equated infinities that are actually different.

12-11-2006, 08:20 PM	#33
tw Read? I only know how to write. Join Date: Jan 2001 Posts: 11,933	I now see the subtle mistake in Shocker's 'cool math trick'. Given S={1, 2, 4, 8 , 16...} and 2S={2, 4, 6, 8, 16, 32 ...}, then 2S + 1 = {1, 2, 4, 8, 16, 32 ...} IOW the infinite set called S and the infinite set called 2S has one less element than the infiinite set called 2S + 1. Yes they are all equal to infinity. But in each case, infinity has a different value. In the case of 2S + 1, the infinity also has one more element. Therefore we have equated infinities that are actually different.

Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)