rational and irrational
Proof. Let be a rational and irrational number. Here we prove only that is irrational — the other cases are similar. If were a rational number , then also would be rational as a product of two rationals. This contradiction shows that is irrational.
Note. In the result, the words real, rational and irrational may be replaced resp. by the words complex, algebraic and transcendental or resp. by the words complex, real and (the last here meaning, as commonly in Continental Europe, a complex number having non-zero imaginary part).
|Title||rational and irrational|
|Date of creation||2013-03-22 14:58:33|
|Last modified on||2013-03-22 14:58:33|
|Last modified by||pahio (2872)|