Intervals

Students can use intervals in answers. The syntax is as follows

Interval	CalcMe word	Equivalent inequality
$left parenthesis a comma b right parenthesis$	`interval_open_open(a,b)`	$a less than x logical and x less than b$
$left parenthesis a comma b right square bracket$	`interval_open_close(a,b)`	$a less than x logical and x less or equal than b$
$left square bracket a comma b right parenthesis$	`interval_close_open(a,b)`	$a less or equal than x logical and x less than b$
$left square bracket a comma b right square bracket$	`interval_close_close(a,b)`	$a less or equal than x logical and x less or equal than b$
$left parenthesis a comma plus infinity right parenthesis$	`interval_open_open(a,+∞)`	$a less or equal than x$
$straight real numbers$	`ℝ`	$straight real numbers$
$left curly bracket a right curly bracket$	`{a}`	$x equals a$
$left curly bracket a comma b comma c right curly bracket$	`{a,b,c}`	$x equals a logical or x equals b logical or x equals c$
$empty set$	`{}`	false $blank$

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	$left parenthesis a comma b right parenthesis union left parenthesis c comma d right parenthesis$
Intersection	$left parenthesis a comma b right parenthesis intersection left parenthesis c comma d right parenthesis$
Difference	$left parenthesis c comma d right parenthesis set minus left parenthesis a comma b right parenthesis$
Complementary	$straight real numbers set minus left parenthesis a comma b right parenthesis$

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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