Prove that the union of two bounded sets is also bounded Pro

Solution

If C is bounded, then we say that m is the upper bound of C.

This means that for all a in C, m > c.

Let\'s say that n is the upper bound of D, so for every b in D, n > d.

Let\'s define k = max(m, n). This means that k>c and k>d, for all a and b. But that means that k is bigger than every number in the union of C and D.

That tells us that k is the upper bound of C union B, so C union D is bounded.