RECENT ASSIGNMENT

MAST20026 Real Analysis
Assignment 2, due before 3pm on Tuesday 15th April
Please submit your assignment to your Monday/Tuesday tutor's box on the ground
oor of the
Richard Berry building (near the northern exit).
Remember to include your name, tutor's name and tutorial time on your assignment.
All students should submit a fully worked solution to these questions.
Please show all working when writing up your solution.
Marks are allocated for working, mathematical accuracy and correct use of logic and symbols. So,
for example, do not use =- when - is meant.
Soliciting answers to assignment questions from internet forums is strictly forbidden.
All proofs should be written in two column format
1. Using the axioms of real numbers prove the following theorem:
8x; y 2 R  (x < y) ) (y < x) _ (y = x)


(Note: This is the theorem that allows us to replace x 6 < y with x  y.)
2. Let x; y 2 R and  2 R
+
. Prove the following theorem:
If x  y +  for any  > 0 then x  y.
For this proof you may assume any theorems stated in lectures.
Hint: Write the theorem as a conditional logic statement (using any necessary quantier(s))
and then consider an indirect proof.
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