Analysis Homework #1
due Thursday, Oct. 21
1. Determine max A when A = {y ∈ R : y = −3x2 + 2x − 1 for some x ∈ R}.
n−1
2. Show that the set B = { 2n+1
: n ∈ N} has no maximum.
n−1
3. Show that the set B = { 2n+1
: n ∈ N} is such that sup B = 1/2.
4. Show that the set C = {x2 : x ∈ R} has no upper bound.
Hint: if y is an upper bound, then y ≥ y 2 and y ≥ 4 > 1.
• You are going to work on these problems Friday in class.
• When writing up solutions, write legibly and coherently. Use words, not just symbols.
• Write your name and then MATHS/TP/TSM on the first page of your homework.
• Your solutions may use any of the results stated in class (but nothing else).
• NO LATE HOMEWORK WILL BE ACCEPTED.