Empty, singleton, finite or infinite set?
Write twelve sets in set notation, from the provinces of Nepal to the months with 32 days, count their members, and sort them by type.
Core concept
In short: Sort collections into empty, single, finite and never-ending sets.
A set is a well-defined collection; a set with no members is empty (∅), one with exactly one member is a singleton, one whose members can be counted to an end is finite, and one whose members never end is infinite
Topic: Sets
A set is a collection of things that is well defined: we can say for certain whether something belongs to it. “The provinces of Nepal” is well defined; “the nice songs” is not, because people disagree. We name a set with a capital letter and list its members inside curly brackets: V = {a, e, i, o, u}. The number of members is its cardinal number, n(V) = 5. Sets come in types. An empty (null) set has no members, written { } or ∅. A singleton set has exactly one member. A finite set has a number of members you can count to the end. An infinite set never ends, so we write “…”: N = {1, 2, 3, …}.
What you will learn
- Explain what makes a collection well defined.
- Write a set in set notation (listing its members).
- Find the number of members of a finite set.
- Classify sets as empty, singleton, finite or infinite.
Before you start
- Know natural numbers, even numbers and odd numbers.
Materials
- A notebook to write the sets
Equipment
- None
Procedure
- Pick a set's card and write it in set notation.
- Count its members.
- Do this for at least eight sets, then sort them all.