Lect 10-Real analysis-IN is not bounded above in IR

UPSC Mathematics (optional) I UP PCS Mathematics I IITJAM Mathematics I Lect 10-Real analysis-IN is not bounded above in IR (proof via LUB property) 8:00.
If zero is less than or equal to ''a'' is less than epsilon, for every epsilon greater than zero, show that a=0. 22:22.
Between any two distinct real numbers there is always a rational number and therefore infinitely many rational numbers (proof) 32:51.
Between any two distinct real numbers there is always an irrational number and therefore infinitely many irrational numbers (proof) 42:30.
@Maths with Asif Khan