- #1

Seda

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## Homework Statement

If A and B are bounded sets, then A U B is a bounded set.

(Prove this statement)

## Homework Equations

Definition of Union is a given.

A set

**A**is bounded iff there exists some real value m such that lxl < m for all element x found in A.

## The Attempt at a Solution

This makes sense to me. If set A is bounded by M and set B is bounded by N, then A U B will be bounded by which value is higher. I have to keep in mind that the definition of a bounded set has the "iff" term.

My attempt (this is quite odd looking to me, I don't know how to make it more straightfoward)

Let x exist in A. Then that means there is a value m where m>lxl by definition of a bounded set.

Let y exist in B. Then that means there is a value n where n>lyl by definition of a bounded set.

Thus, x and y exist in A U B by definition of union.

We know lxl and lyl are < whichever value of m or n is the larger of the two.

We know lxl and lyl are < whichever value of m or n is the larger of the two.

Thus, A U B is a bounded set.

The bolded step seems oddest, but critique on any part of the proof is welcome. Help!