14 Oct '11 21:37>
how do you prove that a decimal that neither repeats nor terminates is irrational?
For example:
0.1411411141114 . . . ,
prove this number is irrational.
For example:
0.1411411141114 . . . ,
prove this number is irrational.
Originally posted by tomtom232One way is to first show the following: every rational number has a terminating or eventually repeating decimal expansion.** Then your claim in question (that a decimal expansion that neither repeats nor terminates is irrational) follows immediately.
how do you prove that a decimal that neither repeats nor terminates is irrational?
For example:
0.1411411141114 . . . ,
prove this number is irrational.
Originally posted by iamatigerI believe it has been done, but it takes some serious mathematics. You don't just have to prove that e and pi are irrational - which are hard enough, but doable - but also that they're a different kind of irrational. Which is, well, obviously true, but non-obvious to prove.
That looks very hard! Are you sure it can be done?