On Saturday, March 30, 2019, William Tanksley, Jr <[email protected]> wrote: > > I'm going to _try_, but this hasn't been peer reviewed... But by > definition the decimal expansion of an irrational has an infinite > number of nonzero digits, while a rational can have a finite number > (ignoring repeating decimals, of course). This means every irrational > whose expansion starts at a given digit is greater than a single > well-defined rational whose expansion simply _is_ that single digit.
Its pretty easy to come up with counter examples of this. Just find an irrational number whose expansion starts with 1 and then find a conflicting rational (perhaps a ratio with 7 in the denominator). Still, it’s an interesting line of thought. — Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
