Let x, y ER such that x
Posted: Sun Jul 10, 2022 11:11 am
Let x, y ER such that x <y. Using the axioms and theorems we have already proven about R, carefully show the following: (a) Find q EN such that: (b) Find p = Z such that: Р q 1 - <y-x. 9 <y≤ Hint. Consider the set S= {k € Z k < qy}. p+1 9 (c) Show that x < <², and conclude that between any two real numbers is a rational number. q'
Posted: Sun Jul 10, 2022 11:11 am
Let x, y ER such that x <y. Using the axioms and theorems we have already proven about R, carefully show the following: (a) Find q EN such that: (b) Find p = Z such that: Р q 1 - <y-x. 9 <y≤ Hint. Consider the set S= {k € Z k < qy}. p+1 9 (c) Show that x < <², and conclude that between any two real numbers is a rational number. q'