You are probably quite certain that the following numbers are irrational. But can you prove it?

a = 0.149162536496481...

b = 0.2357111317192329...

c = 0.1248163264128256...

(In reply to One down, two to go by vswitchs)

It is not obvious that a = 0.149162536496481... is the same fraction as the fraction you provided. Though 266060029582368375943402260274 /    1783692043803805672104863371093
begins with the same given digits, there are an infinite number of possible numbers that 0.149162536496481... could begin.  You have only proven that 0.149162536496481... could be rational.  I propose there exists irrational numbers that begin with the same digits and that the same is true, that the numbers can be the beginning of both rational and irrational numbers, for b and c as well. 

Posted by Dej Mar on 2006-09-06 00:25:27