1. a set is a well defined collection of distinct objects. the objects of a set are called its elements. if a cell has no elements, it is called the empty sets and is deboted by Ø
2. the elements that make up a set can be any kind of mathematical objects.
3. a set which contains all objects, including itself. in set theory as usually formulated, the conception of a universal set b to a russell's paradox and is consequently not allowed.
4. a set A is a subset of a set B if all elements of a are also elements of B; B is then as superset of A. it is possible for A and B to be equal; if they are an unequal then A is a proper subset of B.
5. a null set N C ℝ is a measurable set that has measure zero. this can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length.
