Practice question · Sort into groups
Sort each number by whether it lies in the interval from -2 to 3, including -2 but excluding 3.
Groups: In the interval · Not in the interval
- -2.5
- 2.999
- 3
- 0
- 3.0001
- -2
Hints
- The two endpoints are treated differently, read the wording carefully.
- 2.999 is strictly less than 3, so it qualifies no matter how close it gets.
Show the answer
In the interval: -2, 0, 2.999
Not in the interval: 3, -2.5, 3.0001
Why
The interval is half-open: -2 belongs but 3 does not, however tiny the gap. 2.999 is inside, 3.0001 is outside, and -2.5 falls below the left endpoint. Closeness is irrelevant, only the strict inequality decides membership.
Practise Real Numbers and the Number Line
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