For each set of real numbers below: A = {5":ne Z} 2 B = n² 4n²-1 ER} TER n=1,2,...} 22-3, -2,-1, 0, 1... D={reR: 2³ ≤ 2} (i) State whether or not the set is bounded above and whether or not it is bounded below; (ii) Give the least upper bound (l.u.b.) of the sets which are bounded above and the greatest lower bound (g.1.b) of the sets which are bounded below; iii) State whether or not the l.u.b. and the g.l.b. belong to the corre- sponding set;
For each set of real numbers below: A = {5":ne Z} 2 B = n² 4n²-1 ER} TER n=1,2,...} 22-3, -2,-1, 0, 1... D={reR: 2³ ≤ 2} (i) State whether or not the set is bounded above and whether or not it is bounded below; (ii) Give the least upper bound (l.u.b.) of the sets which are bounded above and the greatest lower bound (g.1.b) of the sets which are bounded below; iii) State whether or not the l.u.b. and the g.l.b. belong to the corre- sponding set;
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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Transcribed Image Text:7. For each set of real numbers below:
A = {5": n € Z}
B =
{2+9:ZER}
n²
=1,2,...}
t
3, -2, -1, 0, 1....
D = {r € R: ³ <2}
(i) State whether or not the set is bounded above and whether or not
it is bounded below;
(ii) Give the least upper bound (l.u.b.) of the sets which are bounded
above and the greatest lower bound (g.l.b) of the sets which are
bounded below;
(iii) State whether or not the 1.u.b. and the g.l.b. belong to the corre-
sponding set;
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