Archive for the ‘Uncategorized’ Category
Astonishing consequences of naive thinking about sets: Cantor's diagonal argument
Posted by: Gary Ernest Davis on: October 4, 2010
I have mentioned in several posts now that many people do not think it is problematic to bundle all the counting numbers together in a set: the set of all natural numbers, denoted . Another apparently harmless naive thought about set formation is that one can always construct the set of all subsets of a […]
What is a triangle? The role of definition
Posted by: Gary Ernest Davis on: October 2, 2010
The Galois field of order 4 is the set with addition and multiplication given by the following tables: Because for every we see that not only addition and multiplication, but also subtraction is always possible in GF(4), although subtraction is trivial since . Also, because we see division, except by 0, is always […]
