# Prove/disprove these two claims

#### Selena

I'm having trouble understanding this pair of claims:

So g is some function whose result is greater or equal to 0... but I don't really get what the rest of the claim means.
Could someone please explain them to me?

#### mathman

Forum Staff
There seems to be something missing. What is O(h)?

#### Selena

O(h) is defined by this, sorry left that out:

The definition of big Oh. f(n) has a slower growth rate than g(n).

#### mathman

Forum Staff
The first one (sum) is true (note that both f and g are non-negative), since if either one grows faster than h, the sum will.

The second one (product) is false, since you can set either f or g = 0 and the other can grow at any rate.