Question

There is no smallest psotiive rational number a porof by contradiciton

Answer 1

In mathematics, there is no smallest positive rational number, as proven by a proof by contradiction. The proof by contradiction method underscores the inherent contradiction arising from assuming the existence of the smallest positive rational number.

Step-by-step explanation:

In the realm of mathematics, we employ a proof by contradiction to establish that there exists no smallest positive rational number.

Let's assume, for the sake of contradiction, the existence of the smallest positive rational number denoted as 'a.'

However, when we divide 'a' by 2, yielding a smaller positive rational number 'b' (specifically 'a/2'), this contradicts our initial assumption that 'a' holds the status of the smallest positive rational number.

Consequently, our assumption of the existence of the smallest positive rational number is deemed false.

The proof by contradiction method underscores the inherent contradiction arising from assuming the existence of the smallest positive rational number, leading to the irrefutable conclusion that there is, in fact, no such smallest rational number in the realm of positive rationals.