1.1.11. Find
(a) sup{a: e R : x
2
+ a ; + l 0 } ,
(b) mf{z = x + x~1 : x 0},
(c) inf{2 = 2* + 2- :x0}.
1.1.12. Find the supremum and the infimum of the following sets:
(a) A = + : m, n G N ,
[ n m J
(c) C
(d)
\ m : ra,neN,
[m + n J
D = i
T ^
: m G Z, n G N i ,
^ |m| -h n. J
f ^ ^
T,T1
= 4 : m, n G N .
(e) E
1.1.13. Let n 3 be an arbitrarily fixed integer. Take all the possible
finite sequences (ai,.. . ,a
n
) of positive numbers. Find the least
upper and the greatest lower bounds of the set of numbers
E:
Ofc
^ afc + afc+1 -f afc+2
where we put an+i = a\ and an+2 = &2
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