[SOLVED] MA3831 Homework 1

Using properties 1, 2, and 3 of the absolute value function on Q stated in class, show that for all x,y in Q:

(i). if ,

(ii) ||x| − |y|| ≤ |x − y| ≤ |x| + |y|.

exercise 2:

Let T = (0,1) ∪ {2}. Find, with proof, supT.

exercise 3:

Let S and T be two bounded above subsets of R. Define the subset

S + T = {x + y : x ∈ S,y ∈ T}.

Show that S + T is bounded above.

exercise 4:

From Abott’s textbook: exercise 1.4.4.

exercise 5:

Using the definition of convergent sequences show that converges to zero.

exercise 6:

Using the definition of convergent sequences show that any constant sequence is convergent.