Describing a set
Choose the set A written as a list of its elements.
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A set can be described in two ways. By listing its elements: A = {1, 2, 3, 6}. Or by a rule that all its elements follow and no other number does: A = {x ∈ ℕ | x is a factor of 6}. Both describe the same set.
What does this generator do?
On easy, it shows a set given by a rule and you pick its elements. On medium it is the other way round: you see the elements and pick the rule. On hard, you list the elements for equations and inequalities in the integers, and sometimes the answer is the empty set ∅.
How to use it
1) Check which numbers x is taken from (ℕ or ℤ). 2) Try the numbers one by one and ask whether each one follows the rule. 3) Watch the ends: with “<” the end number is not included, with “≤” it is. 4) If no number follows the rule, the set is empty.