# Math Help - Compact Set proof

1. ## Compact Set proof

If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact.

how can i prove this?

I know that s1 and s2 are compact which would mean that s1 and s2 are both closed and bounded, and im not sure how to continue this.

2. Originally Posted by p00ndawg
If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact.
how can i prove this?
The unioin of two finite collections is a finite collection.
Any open cover for $S_1\cup S_2$ is a cover for each.
So there is a subcover for each. Their union covers $S_1\cup S_2$.

3. Originally Posted by Plato
The unioin of two finite collections is a finite collection.
Any open cover for $S_1\cup S_2$ is a cover for each.
So there is a subcover for each. Their union covers $S_1\cup S_2$.
ohh i was way over-thinking this.

thanks