Order05 - (Sign Rules in Addition and Multiplication)

The following rules of sign for adding and multiplying real numbers hold:

(positive number) + (positive number) = (positive number),

[This follows immediately from the order property.]

(negative number) + (negative number) = (negative number), [ proof ]

(positive number) x (positive number) = (positive number),
[This follows immediately from the order property.]

(positive number) x (negative number) = (negative number), [ proof ]

(negative number) x (negative number) = (positive number). [ proof ]

See ita-2-2-11-pg20.