Originally Posted by

**bee77** There does not exist a largest negative rational number.

Assume, that there is a largest negative rational number; call it k.

Then 2k, which is the product of two rational numbers, is a negative rational number.

Since 2k is farther from 0 than k is, we have that 2k < k, which implies that k < k/2.

Now, k/2 = 1/ 2 k is the product of two rational numbers.

so k/2 is a negative rational number that islarger than k,

resulting in a contradiction if we sub a value in for K .

Is that ok ?