example of a negative number closed over addition?

Answer 1

Depending on how formal your instructor wants your answer to be, I will list this two ways.

Basic Answer:

Any combination, by addition, of two negative numbers, X and Y will always be negative. So, if X,Y <0, then X+Y <0 for all negative numbers.

Formal Answer:

Let R^- denote the set of all real, negative numbers, and x, y ∈ R^-.

Since x,y ∈ R^- , we can state that x, y < 0. Therefore,

x + y < x + 0 = x < 0 for all x,y.

In conclusion, x + y ∈ R^- for all x,y ∈ R^-.