Bounds If for all numbers x of a set there is a number M such that x s M, the set is bounded above and M is called an upper bound. Similarly if x 2 m, the set is bounded below and m is called a lower bound. If for all x we have m s xs M, the set is called bounded. If M is a number such that no member of the set is greater than M but there is at least one member which exceeds M - e for every e >0, then M is called the least upper bound (l.u.b.) of the set. Similarly, if no mem- ber of the set is smaller than m +e for every e >0, then m is called the greatest lower bound (g.l.b.) of the set.

Bounds If for all numbers x of a set there is a number M such that x s M, the set is bounded above and M is called an upper bound. Similarly if x 2 m, the set is bounded below and m is called a lower bound. If for all x we have m s xs M, the set is called bounded. If M is a number such that no member of the set is greater than M but there is at least one member which exceeds M - e for every e >0, then M is called the least upper bound (l.u.b.) of the set. Similarly, if no mem- ber of the set is smaller than m +e for every e >0, then m is called the greatest lower bound (g.l.b.) of the set.

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Description: is the textbook missing a line?should this statement be inserted? "if no member of the set is smaller than m, but there is at least one member that is smaller than....why or why not? BoundsIf for all numbers x of a set there is a number M such that

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given 5 persons, namely A, B, C, D, and E, are to be seated on 5 chairs arranged side by side in a straight line and are labelled as in Figure 1. 1 2 3 4 5 Figure 1: 5 chairs side by side in a straight line The following rules are specified. The predicate OnChair (P, s) means that I is seated on chair of number s. T₁: 72: VX, Y, s OnChair (X, s) A OnChair(Y,s) → X = Y Vs, t OnChair (A, s) A UnChair (B, t) →> |s-t|/1 T3: Vs, t OnChair(B, s) A OnChair (C, t) → |s-t|=1 T4: Vs OnChair(D, s) V OnChair(E, s) → s/1^s/5 TS: Vs, t OnChair(C, s) A OnChair (D, t) → |s-t| / 1 TG: Vs,t OnChair(A, s) A OnChair (E, t) →> |s-t=2 s and t represent any chair number; X and Y represent any person sitting on a chair. As examples to interpret the rules, • ₁ means if person X is sitting on chairs and person Y is also sitting on chair s, X and Y refer to the same person, i.e. no two persons can be seated on the same chair; 72 means A and B cannot be seated next to each other. Assuming B is to be seated on…