Can the product of two positive numbers be less than either number?

Answer 1

The smallest positive number is 1. Since every positive number multiplied by 1 is the number itself as a product, then the product is neither less than 1 nor less that positive number. We can say the same for all the products of all other positive numbers.

However, we can prove it:

Let n, m > 0. Let suppose that nm < n or nm < m. So,

nm < n divide by m to both sides;

n < n/m is not true

nm < m divide by n to both sides;

m < m/n is not true

Thus, the product of two positive numbers is always bigger than its factors.

Answer 2

PPP