- #1
cragar
- 2,552
- 3
Homework Statement
Show that if [itex] a\in\mathbb{Q} [/itex] and [itex] t\in\mathbb{I} [/itex]
then [itex] a+t\in\mathbb{I} [/itex] and [itex] at\in\mathbb{I} [/itex]
as long as a≠0
The Attempt at a Solution
Let [itex] a=\frac{x}{y} [/itex] where x and y are integers. and t is an irrational number
If I have a+t . since t cannot be written as a fraction, there's no way an integer times an irrational number will be an integer so this number will be irrational. and also at and a+t would be irrational.