Letters of the alphabet {a, b, c} Coins: {penny, nickel, dime} Counting Numbers {1, 2, 3, ...} Positive Even Numbers {2, 4, 6, ...}
Elements of sets:
Each element separated by commas Elements use the element symbol ∈ In the set S = {1, 2, 3} 1 ∈ S, 2 ∈ S, 3 ∈ S
Cardinality of a set:
Measures how many elements Given a set S, cardinality = |S| With S = {1, 2, 3}, |S| = 3 since S has 3 elements
Special Type of Sets:
The Universal Set U has every element The empty set ∅ has no elements
Complement of a set:
Everything not in the set but in U Write this as S' or SC Given U = {1, 2, 3, 4, 5} and S = {1, 2, 3} SC = {4, 5} since they are in U not in S
Finite sets:
Finite sets have countable elements. {1, 2, 3} for example has 3 elements
Infinite sets:
Infinite sets have uncountable elements They go on forever using ...symbol {1, 2, 3, ...}
Set Notes:
Element order does not matter {1, 2, 3} = {3, 2, 1}
How does the Sets Calculator work?
Free Sets Calculator - This lesson walks you through what a set is, how to write a set, elements of a set, types of sets, cardinality of a set, complement of a set.
What 5 formulas are used for the Sets Calculator?
Set is denoted with braces and commas separating elements {1, 2, 3} Elements are members of items in a set S = {1, 2, 3}, 1 ∈ S S = {1, 2, 3}, the cardinality |S| = 3 since S has 3 elements The empty set ∅ contains no elements Given a Universal Set U = {1, 2, 3, 4, 5} and S = {1, 2, 3}
SC = {4, 5} since they are everything in the Universal set not in S
What 11 concepts are covered in the Sets Calculator?
cardinality
a measure of the number of elements of the set
coefficient
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
difference
the result of one of the important mathematical operations, which is obtained by subtracting two numbers
element
an element (or member) of a set is any one of the distinct objects that belong to that set. In chemistry, any substance that cannot be decomposed into simpler substances by ordinary chemical processes.
index
an indicator, sign, or measure of something
intersection
the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. A ∩ B
product
The answer when two or more values are multiplied together
set
a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
sets
subset
A is a subset of B if all elements of the set A are elements of the set B