Question

(2- Lat S= La Ahor thati .S (6) Prove that S a broundal Ast Lub(s)? (c) Hor o Anorr that S Ao d) Hou do swe tenour tht Sh gl.b (5)? te numbu lub (s) (e) Fnd lub(s) Tuoe (4) Fnd glb(s) and L SR. Proe hat So ound ast nd on thue i numbw M Sit xs M fal XeS

Answer 1

ur s c-1 (2-4 1nen3 20 Ca) tor (1) ( 2 4 ES 2.' ES (1 2 2 2 - 4 since > o 2n 25 ounded set Cc) since sia boundedl 3ub setof R S bounded ab ove, lub (s) has an belou boun ded also Shas a 916 CS)

e)Claim Cus show (b) is of s an npper bound Let 2-E be Less thaan meal number any EYO Then Since 4 3 NENN st <E neN for eren some 2-4 (2-44 2n upper tound 2-E io not an pper baund.o S least 2 i the

Similary as showed in Cb) - 2 s Lower oun ol for s a then Since 4 3 NEN st 4 nrN 2n 2 for Some odd neN S 2-4 4 - 2 -2+E 25 - 2+E is not lower oound for a - 2 in the greatest Lower bound for