Question: LetXbe a nonempty set and letbe a linear ordering onX. Prove that every nonempty finite subsetSXcontains a-greatest element, i.e., there isx_0Ssuch thatxx_0for allxS.Hint.Prove this by

LetXbe a nonempty set and letbe a linear ordering onX. Prove that every nonempty finite subsetSXcontains a-greatest element, i.e., there isx_0Ssuch thatxx_0for allxS.Hint.Prove this by induction on the size of the finite setS. Note that ifShasn+1 element, then by removing a single element you obtain a set of sizen.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Please help with problem 7. References are below the image. 7. 14 points Let @ be a nonempty collection of subsets of a nonempty set X and a subset B C X be arbitrary. Prove that (a) r(6n B) = (6)n...

Let X be a nonempty set, A a collection of nonempty subsets of X, and C a choice correspondence on A. Recall the following axioms. (a) (Axiom ) If S,TA and TS, then C(S)TC(T). (b) (Axiom ) If...

Question 3: This is a long question. Don't be intimidated! As always, for each part in this question, you must justify your answer. Professor Justin Bieber needs a data structure that maintains a...

the whole question is this. s1,s2...s15 are in the second photo. Task 6 (1.5 pt) Provide a partition of the set of functions below with respect to the relation: two functions belong to the same...

i mainly need help with how to do nine and what the graph would look like so if you could explain it that would be great. Problem 1: A 3-foot-tall monkey is in a room where some bananas are suspended...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

#2. Let D be a nonempty set and suppose that f: D R and g: D R. Define the function f + g: D R by (f + g)(x) = f(x) + g(x). Recall that sets f(D), g(D), and (f + g)(D) are the ranges of f, g, and f +...

Write Grafstate code for a context-free grammar that is equivalent to N. Your Grafstate code Type your answers in a Grafstate file (.graf.txt) must run with no errors. We defined a context-free...

Let .x1.......xn be distinct real numbers. Prove that the n Ã n matrix K with entries

Remember, a bar scale shows graphically the ratio of map units to ground units. The top scale shows the comparable ground measurement in kilometers (km) and the bottom bar scale shows the comparable...

We have two bonds that have an identical time to maturity and coupon rates. On is callable at 1 1 7 , the other is callable at 1 2 0 . Which must have the higher yield to maturity? The 1 1 7 one The...

Klassen Toy Company, Inc., assembles two parts (parts 1 and 2): Part 1 is first processed at workstation A for 15 minutes per unit and then processed at workstation B for 10 minutes per unit. Part 2...