Question

Billy is trying to convince Sam that all square roots are irrational. To support his argument, Billy points out that , , , and are all irrational. Since this set of numbers contains the square roots of both prime and composite numbers as well as even and odd numbers, Billy argues that there is no number (prime, composite, even, or odd) whose square root is rational. Thus, all square roots must be irrational where has billy made his error????

Answer 1

in the ,,,,,, that list contained no numbers such that their square root is rational

Answer 2

Looks like an inductive fallacy to me. For instance, if I asked you to prove S_n = (n(n+1))/2, you would't just bang out a few examples and say QED, right? You would have to show it is correct for all natural numbers n. All Billy is doing is providing examples examples which seem to support his conjecture, but he hasn't proved his conjecture is true for all possible values of the number categories he listed.

Answer 3

Its like I claimed that everyone in the world has black hair.

Then I supported this by saying that "look bob has black hair, and john has black hair, and I have black hair, so everyone must have black hair"