Sets

• Set Theory - Is a branch of mathematical logic where we’ll learn sets and their properties.
• Sets - Collection of objects or group of objects. These objects are often called elements or members of a list.
• Set Theory Origin - Father of Sets is Georg Cantor (1845 - 1918). He is a German mathematician that initiated the concept of set theory or theory of set. While working on a problem on trigonometric series he encountered sets that have become the most fundamental concept in mathematics. Without understanding sets it would be difficult to explain other concepts such as relations, functions, sequence, probability, etc.
• Within a set each individual object is known as a member or element.
• Ellipses mean to continue, when we put it at the end or beginning of a set it means that our set is an endless list of elements.
• Cardinality - Describes the size of the set.
• Sets are represented in curly braces. The element of a set is deficit in either statement form, roster form, or set builder form.
• When we say statement form, the well-defined members of a set are written or enclosed in curly braces.
• In roster form all the elements of a set are listed.
• Set Builder Form - It is also used to express sets within intervals or an equation. This is used to write and represent the element of a set often for a set with an infinite number of elements. The general form is, A = {x: property}.
• Null Sets - A set that does not contain any element.
• Symbol of Null Set is called phi.
• Singleton Sets - A set which contains a single element.
• Finite Sets - A set which contains a definite number of elements (may katapusan).
• Infinite Sets - (walang katapusan). Maybe applicable on roster form.
• ⊆ - Subsets have few or all elements equal to the set.
• ⊄ - Not Subset - left set is not a subset of right set.
• ⊂ - Proper Subset - Subset has fewer elements than the set.
• ⊃ - Proper Subset - set A has more elements than set B.
• ⊇ - Superset - set A has more elements or equal to the set B.
• ⊅ - Not Superset - set X is not a superset of set Y.
• = - Equality - both sets have the same members .
• Universal Sets - This is a set which contains the element of all related sets without repetition.
• Union of Sets - Is the set that contains all the elements that belong to either A or B or both. It represents the combination of all distinct element forms of both sets. (A ∪ B)
• Intersection of Sets - Is the set that contains all the elements that are common to both A and B. (A ∩ B)
• Complement of Set - Is the set that contains all the elements that do not belong to A within a given universal set. (A^c)
• Cartesian Product - The set of all ordered pairs, A and B, where a is an element of A and b is an element of B. (A x B)
• Set Difference - That contains all the elements belonging to A but not to B. It represents all the elements that are exclusive to A. (A - B)
• Venn Diagram - Another representation of sets. An illustration that uses circles that shows the relationship among things or finite groups of things. 
• | - such that
• : - such that
• ∀ - for all
• ∃ - there exists
• ∴ - therefore
• • N: Set of all natural numbers
• • Z: Set of all integers
• • Q: Set of all rational numbers
• • R: Set of all real numbers
• • Z+: Set of all positive integers