Transcript The set of all real numbers

Any well-defined collection of
objects and each object of the
collection is an element or member
of the set
Example:
All the planets in the
solar system
elements:
Mercury, Venus, Earth, Mars,
Jupiter, Saturn, Uranus and
Neptune
Two Kinds of Sets
a. Finite sets
If and only if there is a number that describes exactly
how many elements it contains
Example:
The set of all the vowels of the
alphabet
Two Kinds of Sets
b. infinite sets
there is no exact number that describes exactly how
many elements it contains
Example:
The set of all real numbers
c. Empty or null set
The set containing no elements and denoted by { } or
Ø
Ways of representing a set
a. Roster notation
•If the collection does not contain a very large number
of objects
•All the elements are listed and enclosed them between
a pair of braces
Example:
All the vowels of the alphabet
A ={ a, e, i, o, u}
•Read as “the set whose elements are a, e, i, o, u.”
Exercises:
1. All months of the year having exactly 30 days
2. All suits in a deck of playing cards
3. The squares of the first four natural numbers
Ways of representing a set
b. set-builder notation
•If the collection contains a very large number of objects
•Tells what requirements must be met in order to belong
to the set
Example:
All the countries in the world
A ={ x| x is a country in the world }
•Read as “the set of all x’s such that x is a country in
the world”
Exercises:
1. All the positive multiples of 3
2. All the states of the Unites States
3. All even natural numbers
Exercises:
Represent each set using the roster method.
1. All the types of clouds
2. All the distinct letters in the word “Mississippi”
3. All natural numbers less than 5
4. Students in the class who are not from cebu
5. The children of your parents
Exercises:
Represent each set using the set-builder notation.
identify the set as either finite or infinite.
1. {2, 4, 6, 8, 10, …}
2. {Mercury, Earth, Mars, Neptune, …}
3. {5, 10, 15, 20, …}
4. {Macapagal, Garcia, Magsaysay, Quirino, …}
5. {Philippines, Panama, Puerto Rica, …}