# Intervals

Students can use intervals in answers. The syntax is as follows:
Interval CalcMe word Equivalent inequality `interval_open_open(a,b)` `interval_open_close(a,b)` `interval_close_open(a,b)` `interval_close_close(a,b)` `interval_open_open(a,+∞)` `ℝ` `{a}` `{a,b,c}` `{}` false

To enable intervals, in Validation > Allowed input set mode General and then in Options set Intervals.

It is possible to do operations with intervals.

Operation Example
Union
Intersection
Difference
Complementary

The student answer can have operations, and it will be simplified and compared with the correct answer. If you want to prevent this, set is simplified in Validation > Additional properties, as usual.

Intervals are conceptually equivalent to inequalities, but internally (in the Algorithm) they are different data types. If in Validation > Comparison with student answer you use the default Mathematically equal then student answer must be of same type than the correct answer. Alternatively, if you set Equivalent equations then students can answer either intervals or inequations.

If you want to make an algorithm for a question with intervals, you can not use the interval symbols directly; you must use the corresponding CalcMe word for them. See the table above. There are commands that return intervals; for instance `domain_set()`. Other commands return inequations; for instance `domain()`. You can convert the result from inequations to intervals using `expression_to_set()`.

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