22 Feb '08 22:38

Question one: Does these exist a real number 'a' such that a*Pi is a rational number? (NOTE: a rational number is a number that can be written in the form a/b, with a and b both integers, incase you were wondering...)

Question two: (my mind wandered onto this whilst contemplating the above question. I'm not too sure of the answer, but I have a hunch...)

The cardinality (essentially, size) of the real numers is "uncountably infinite", whilst the cardinality of the rational numbers is "countably infinite". That is to say, there does exist a bijection from the natural numbers into the rational numbers but

My question is this; imagine a circle of

Question two: (my mind wandered onto this whilst contemplating the above question. I'm not too sure of the answer, but I have a hunch...)

The cardinality (essentially, size) of the real numers is "uncountably infinite", whilst the cardinality of the rational numbers is "countably infinite". That is to say, there does exist a bijection from the natural numbers into the rational numbers but

*not*into the real numbers.My question is this; imagine a circle of

*countably*infinite diameter. Is it's circumference countably of uncountably infinite? Or is this a really stupid question without an answer? I feel it is the latter (really stupid...), but I'm not sure.