# Another bounded proof

• Mar 11th 2007, 01:17 PM
tbyou87
Another bounded proof
Prove that if B subset A subset Real #'s and A is bounded, then B is bounded.

Proof attempt:
Assume B subset A subset Real #'s and A is bounded.
Then a <= u for all a element A and l <= a for all a element A, where u is upper bound and l is lower bound.
Since B subset A, every x element B => x element A.
Then a <= u for all a element B and l <= a for all a element B.
Therefore, B is bounded.

I was wondering if this was correct, and if it is not how I can fix it if possible.
Thanks
• Mar 11th 2007, 01:33 PM
CaptainBlack
Quote:

Originally Posted by tbyou87
Prove that if B subset A subset Real #'s and A is bounded, then B is bounded.

Proof attempt:
Assume B subset A subset Real #'s and A is bounded.
Then a <= u for all a element A and l <= a for all a element A, where u is upper bound and l is lower bound.
Since B subset A, every x element B => x element A.
Then a <= u for all a element B and l <= a for all a element B.
Therefore, B is bounded.

I was wondering if this was correct, and if it is not how I can fix it if possible.
Thanks

It looks more or less OK to me

RonL