Is the product of 2 positive numbers greater than either number?

Answer 1

Not always. Here are counterexamples:

Cases involving 1:

1 x 1 = 1

1 x 3 = 3

Cases involving positive numbers less than 1:

0.5 x 10 = 5

0.5 x 0.5 = 0.25

Note that here we have positive numbers that are less than or equal to 1. When either number is less than 1, the product will not be greater than both numbers. Also, if either number is equal to 1, the product will be equal to the larger of the original numbers.

A modified statement is the product P of two positive real numbers x and y such that x, y > 1, is greater than both x and y.