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 •