QuestionQuestion

Transcribed TextTranscribed Text

1. Use only the field and order axioms to prove the following statements for .2, y, Z € R. Make sure you indicate which axiom you are utilizing at each step. (a) Prove that if r > 0 and y > 0, then x + > 0. (b) Prove that if r > 0 and y > 0, then xy > 0. (c) Prove that for z + 0 and y + O,then (d) Prove that 0 is its own additive inverse, i.e. 0 - -0. (c) Prove that 1 is its own multiplicative inverse, i.e. 1 (f) Prove that r - y - 0 iff r - y. (g) Prove that if xy - Z and any two of x,y and Z are positive, then the third real number must also be positive. (h) Prove that if . > 0 then also =-1 > 0. 2. Given that [ - { -r, x, if 0 if x 0 prove the following statements for z, y € IR : (a) 0 for all I € IR: and - 0 iff 7 - 0. (b) [ - 1-z% (c) - I < (d) S y - -y S Z y. (e) x - y . (f) ||x| - [y| 1s/2+y/. 3. For the following sets A, find (if they exist) max A, min A, (sup A, inf (A) : (a) A - {1,3,9,4,0} . (b) A - [0,00). (c) A - [-1,3] - (d) A - {x:-2 - 1 - -0}. (e) A - {x R: I2 < 2}. (f) A - (-00,00) . (g) A - } -

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    50% discount

    Hours
    Minutes
    Seconds
    $3.60 $1.80
    for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Real Analysis Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats