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Syntax
Reading time: 1minThe interval notation is quite particular. You can create several intervals with the syntax you can see below.
The interval notation is quite particular. You can create several intervals with the syntax you can see below.
| Interval | CalcMe word | Equivalent inequality |
|---|---|---|
| (a,b) | interval_open_open(a,b) |
a<x∧x<b |
| (a,b] | interval_open_close(a,b) |
a<x∧x≤b |
| [a,b) | interval_close_open(a,b) |
a≤x∧x<b |
| [a,b] | interval_close_close(a,b) |
a≤x∧x≤b |
| (a,+∞) | interval_open_open(a,+∞) |
a≤x |
| ℝ | ℝ |
ℝ |
| {a} | {a} |
x=a |
| {a,b,c} | {a,b,c} |
x=a∨x=b∨x=c |
| ∅ | {} |
false |
Furthermore, it is also possible to do operations with intervals.
| Operation | Example |
|---|---|
| Union | (a,b)∪(c,d) |
| Intersection | (a,b)∩(c,d) |
| Difference | (c,d)∖(a,b) |
| Complementary | ℝ∖(a,b) |
The student's answer can have operations, and it will be simplified and compared with the correct answer. If you want to prevent this, set Simplified in Validation options > Simplification, as usual.
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().
