Question
Are there more rational or irrational numbers?
I am thinking irrational, because the product of a rational and irrational number is irrational. Is this enough of a reason to prove it?
I am thinking irrational, because the product of a rational and irrational number is irrational. Is this enough of a reason to prove it?
Answers
Steve
There are many many more irrationals than rationals. In fact, there are so many more that if you threw a dart at the number line, the chance of hitting a rational is zero.
The proof is relatively simple, and involves the idea of countability. You can count the rationals, but not the irrationals.
The proof is relatively simple, and involves the idea of countability. You can count the rationals, but not the irrationals.