Question

need help in SEQUENCE....
i did not understand 'least upper bound' and 'greatest lower bound'

Answer 1

@amistre64

Answer 2

if something is 6 feet tall, is it less than 50 feet tall? less than 45 feet tall? less than 22 feet tall?

there are an infinite number of upper bounds that we can attribute to this object. the least of those uppers will be the closest, or best attribute, to define it

Answer 3

is it l.u.b 7 feet here?

Answer 4

id say the lub is 6 feet :)

it less than 6.0000000000000000000000000000001 feet

etc ..

Answer 5

now i saw a problem in my book...
for the set {1,1/2,1/3,....,1/n,....}
lub is 1 and glb is 0 ....why?

Answer 6

can it ever be larger than 1?

Answer 7

no...

Answer 8

then 1 is the least upper boundary for it

as n gets larger, the values get smaller and smaller and approach 0 right? can they ever be less than 0?

Answer 9

okay..
S={1/2,2/3,3/4,4/5.....n/(n+1).....}
lub=1 i got it...but
glb=1/2...what about this?

Answer 10

since the sequence starts at 1/2 and progressively gets larger; then how small can it get?

Answer 11

oh...
yeah i got it...

Answer 12

thanks for the help...:)

Answer 13

youre welcome