Non-Positive and Non-Negative Numbers

The word _negative_ has been replaced by _non-positive_ in the following facts about negative numbers. Which of these statements are still true for non-positive numbers? Indicate **all** such statements.

That's right! [[snippet]] Since the sum of negative numbers is negative, you only need to consider what happens when adding 0. Adding 0 does not change the value, so the sum of two non-positive numbers will always be non-positive.

Incorrect. [[snippet]] Non-positive numbers include 0, and the product of any number and 0 is 0. Since 0 is not positive, the product of two non-positive numbers does not need to be positive.

Incorrect. [[snippet]] Division by 0 is undefined, so $$\frac{1}{x}$$ is undefined when _x_ = 0, which is a non-positive value.

The sum of two non-positive numbers is non-positive.

The product of two non-positive numbers is positive.

$$\frac{1}{x}$$ is defined for all non-positive values of _x_.

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