No.
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Real numbers are all positive numbers except zero.
Any positive number can be written as a quotient of two positive numbers or a quotient of two negative numbers. Any real number can be written as the quotient of two real numbers.
No, the product of two negative numbers is always a positive.
Positive numbers are greater than zero and negative numbers are less than zero. They are both collectively referred to as real numbers.
Not at all. The class of "natural" numbers are all positive, but the classes of "real" numbers and "rational" numbers include negative numbers.