Hi, I'm having trouble to write a formal proof for the following.
1. Let . Show that does not exist for any a
*EDIT* I deleted the second problem so I could posted without double-posting
Hi, I'm having trouble to write a formal proof for the following.
1. Let . Show that does not exist for any a
*EDIT* I deleted the second problem so I could posted without double-posting
#1. First say . Suppose that then (by picking ). But since the is a rational with for no matter it would mean that and so this is a contradiction. If then choose and apply same argument. If then it means for all . Take then and it would mean for all , but since there is irrational then it would mean which is a contradiction.