Tuesday, September 18, 2018

algebra precalculus - What does the notation in this claim, that needs to be proved, mean?



Prove, or disprove using a counter example:


Let $p,q\in\mathbb{R}$ \ $\mathbb{Q}$ \, then $p-q$ is irrational.


I don't understand what the back slash between the $\mathbb{R}$ and $\mathbb{Q}$ means.


Answer



The $\setminus$ sign means substraction of sets. $$A\setminus B = \{x\in A \mbox{ such that } x\not\in B\}.$$


In your case, $\mathbb{R}\setminus\mathbb{Q}$ is the set of irrational numbers.


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