Being transcendental implies necessarily being irrational?
Is a transcendental number necessarily irrational?
-3
$\begingroup$
elementary-number-theory
irrational-numbers
-
0Dear dot dot, we do not delete questions which already have answers (much less when the answers have been upvoted this much!) because at that point it would result in the work of the *answered* being deleted along with the question. – 2012-04-06
1 Answers
19
Yes. If it were rational, then it would be the root of a degree one polynomial.
-
0"Polynomials have precise definitions" is somewhat a matter of convention and habit. Beyond that there is only logical consistency. The question is whether these definitions stand in the light of new data. Please see the reference to geometry in the question "Is the diagonal of a square truly irrational?" – 2013-06-07