# 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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