Question 5. (15 marks) Consider the set of all real numbers r such that
-00 < r ≤ -1.
(a) Is this set bounded?
(b) Give two different upper bounds.
(c) Find the supremum of this set.
Justify your answers.

 

Question 4. Consider the following subsets of the real numbers. I'l write No for the set of positive integers. A- -1,5.2, 1,3.7) B=[2.3)-(x E R : 2 3) に1 G-cos(n) nEN H-(100n-n2 : n EN) Determine which of these sets have upper bounds. For each set that has an upper bound give two different upper bounds and say what you think the least upper bound is. If you are confident of what the least upper bound is then prove it, otherwise just say that you can't prove it. Note that for a mathematician "confidence of truth" "ability to prove".

Consider the following. (-infinity, 1) (a) Give a verbal description of the subset of real numbers represented by the interval. The interval is the set of all real numbers less than or equal to 1. Interval is the set of all real numbers less than 1. The Interval is the set of all real numbers greater than 1. The Interval is the set of all real numbers. The Interval is the set of all real numbers greater than or equal to 1. (b) Sketch the subset on the real number line. (c) State whether the interval is bounded or unbounded. The interval it bounded. The interval is unbounded.

Consider the following. (-infinity, 1) (a) Give a verbal description of the subset of real numbers represented by the interval. The interval is the set of all real numbers less than or equal to 1. The interval is the set of all real numbers less than 1. The interval is the set of all real numbers greater than 1. The interval is the set real numbers. The interval is the set of all real numbers greater than or equal to 1. (b) Sketch the subset on the real number line. (c) State whether the interval is bounded or unbounded. The interval is bounded. The interval is unbounded.