Question

Show that (x,y)contains infintely many irrationals

Answer 1

how do you define an irrational in tuple (x,y)?

Answer 2

Maybe he means to show that the space R^2 is contained quite a few irrationals ....

Answer 3

Or maybe an open interval (x, y) is meant by him....

Answer 4

possibly that ...

Answer 5

this is given by irrational density theorem

Answer 6

I know that there is a way to show how many irrationals are placed between a and b ...

Answer 7

you need to show that they are rational irrational. Dang!! can't copy my own wordpress post :((

Answer 8

It is possible to show that there is, at least, an irrational number between the two real numbers a and b ...

Answer 9

well ... that is the problem.

Answer 10

there are 4 cases. considering 'a' and 'b' to be rational or irrational.

Answer 11

looks like this is more simple then how I did.
http://en.wikibooks.org/wiki/Real_Analysis/Properties_of_Real_Numbers