Introduction to analysis homework questionssee attached for questionsplease type your answerProblem 2.5.8: Let A = {0,1,2} and B = {-8,3,6}. Describe the

following sets by writing all elements: A + B, AB, A + (-1)A.

(Note that A – B is a set theoretic notation defined in Definition 1.1.1

part (5). In particular, A + (-1)B # A- B, and A – A = 0.)

Example 2.5.1: Please make clear of the distinction between inf and

min, and between sup and max. min[-1,8) = -1 = inf[-1,8). On the

other hand, we have sup[-1,8) = 8 while max[-1,8) does not exist.

Problem 2.5.1: Suppose S is a nonempty subset of R that is bounded

below. Let us denote the set{-s:E S} by -S.

(1) Prove that -S is bounded above. (Hence, sup(-s) exists by the

completeness axiom.)

(2) Prove that:

(i)-sup(-S)is a lower bound of S, and

(ii) if a E R is a lower bound of S, then a s-sup(-s).

Therefore, we have shown that if S is a nonempty subset of R that is

bounded below, then infs exists, namely infs = -sup(-s).

1. Problem 2.5.1. (Note that the set – defined here is the same set as (-1) defined in

Problem 2.5.8. So, you may want to read Problem 2.5.8 before you do this problem.)

Part (1) 5 points.

Part (2)

5 points

Purchase answer to see full

attachment

#### Why Choose Us

- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee

#### How it Works

- Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the "
**PAPER DETAILS**" section. - Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “
**CREATE ACCOUNT & SIGN IN**” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page. - From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.