- #1
epkid08
- 264
- 1
Is there a variant form of induction to prove something about the rationals as opposed to just the natural numbers?
You could start by proving it for the open interval (0, 1) by showing that for an arbitrary integer m, m < n, [tex]P(\frac{m}{n}) \Rightarrow P(\frac{m}{n+1})[/tex], for all natural numbers n, and then extend the domain to all positive rationals.
Is this even plausible?
You could start by proving it for the open interval (0, 1) by showing that for an arbitrary integer m, m < n, [tex]P(\frac{m}{n}) \Rightarrow P(\frac{m}{n+1})[/tex], for all natural numbers n, and then extend the domain to all positive rationals.
Is this even plausible?