Question

If A,B subsets of R is bounded, then show that AUB also bounded.

Answer 1

let \( a_1 \) be upper bound of A and \( b_0 \) be upper bound for B,
if \( a_1 > b_1 \) then \( a_1 \) is bound for B also, so \( a_1 \) is bound for AUB
if \( b_1 > a_1 \) same case

do same for lower bounds

Answer 2

*similar case

Answer 3

why your answer appears [Math Processing Error].
But i know what is it..let x be upper bound of A and y be upper bound for B..like this?

Answer 4

yes

Answer 5

ok, now it can read..thanks

Answer 6

A is bounded means that there is K>0
\[
a\in A \text { implies } |a| \le K
\]

B is bounded means that there is H>0
\[
b\in B \text { implies } |b| \le H
\]
Let G= K + H
\[
c\in A \cup B \text { implies } |c| \le G
\]

Answer 7

kinda remembered that ... ty prof!!

Answer 8

yw

Answer 9

You can of course also take G=Sup{H,K}.

Answer 10

thanks guys..

Answer 11

yw