if is irrational then is irrational
If be a real number and is an integer such that is irrational, then is irrational.
Let be rational. Then there exist integers and with such that . Thus, , which is a rational number. ∎
Note that the converse is not true. For example, is irrational and is rational.
|Title||if is irrational then is irrational|
|Date of creation||2013-03-22 14:18:50|
|Last modified on||2013-03-22 14:18:50|
|Last modified by||Wkbj79 (1863)|