Lesson 2: Language Of Sets Flashcards
lt is often said that mathematics is the language of?
Science
the set of natural numbers?
= {1,2,3,4,5,…}
The set of whole number?
={0,1,2,3,4,5,…}
The set of integers?
={…-2,-1,0,1,2,…}
The set of rational numbers?
={m/n, where n ≠ 0 }
The set of irrational numbers?
={non-repeating, non-terminating decimals}
includes the numbers used for counting:
The set of natural numbers
is the set of natural numbers plus zero:
The set of whole numbers
adds the negative natural numbers the set of whole numbers:
The set of integers
includes fractions written as (m/n|m and n are integers and n ≠ 0)
The set of rational numbers
is the set of numbers that are not rational, are non repeating, and are non-terminating:
(h|h is not a rational number).
The set of irrational numbers
a collection of objects
Set
the objects in a set are called the
elements of a set
“x” is called a?
Variable
symbol used to represent any element of a given set.
Variable(x)
Another way of writing the above set S is to use what is called
set-builder notation
vertical bar (|) is used in place of words?
Such that
is used in place of words such that
vertical bar (I)
are used to indicate that the list goes on and on with no last number.
Dots
The symbol “ ∈ “ is used to indicate that a specific element belongs to a set.
Element
A. Types of Describing Sets:
- Rule method
- Roster method
describe the elements of the set.
Rule method
List the element of set
Roster method
Types of set:
- Finite set
- Infinite set
- Unit set
- Null set
The number of set in countable
Finite set
The number of set is not countable
Infinite set
a set composed of only one element.
Unit set
a set composed of no element.
Null set
refers to the number of elements of a given set.
cardinality
A is a subset of B “A c B” if every element of A is an element of B.
Subset
A and B have the same number of elements.
Equivalent Sets
A and B are equal sets, A = B, if A and B have the same number of elements.
Equal Sets
sets if A and B have no common elements.
Disjoint Sets
Created venn diagram
John venn
make mathematics easier because they help us to see the whole situation at a glance.
Diagrams
This larger set is called the
universal set.
Symbol of universal set?
U
is a rectangular figure representing the universal set
venn diagram
Operation sets:
- Complement
- Union
- Intersection
- Set difference
- Cartesian product
the set that contains the elements in U but not in A.
Complement
is the set composed of the elements in A or in B or both.
Union
is the set composed of elements both in A and B.
Intersection
A - B is the set composed of the elements of A not found in B
Set difference
is the set of all ordered pairs (a, b), where a is in A and b is in B.
Cartesian product