(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof about rational numbers.

**Physics Forums | Science Articles, Homework Help, Discussion**