Practice question · Select all that apply
Select every statement that is TRUE.
Hints
- For the second claim, try adding an irrational number to its own negative.
- For the last claim, recall what 1/3 looks like as a decimal.
Show the answer
- A. The rational numbers are countable
- C. The sum of two rational numbers is always rational
- E. Between any two distinct real numbers there is a rational number
Why
Rationals are closed under addition (common denominators keep everything a ratio of integers), they are dense in the line, and they are countable. But the square root of 2 plus its negative is 0, so irrationals are not closed under addition, and 0.333... is a non-terminating rational.
Practise Rational and Irrational Numbers
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