An element is a distinct entity which is a member of a set. This means that an element is anything that can be named, measured, and contained within a set.
A set describes a collection of elements, or distinct independent entities. Grouping elements together in sets is how we define relationships between otherwise unrelated entities.
A symbol which correlates an element to a set it belongs to. This may be read: "the element x is a member of set A." An element can belong to multiple sets; but, a set may only contain one of each element.
A symbol which represents the exclusion (or the disconnection) of an element from a set. This may read: "the element x is not a member of set A."
Equality is how we express similarity, or likeness between distinct entities. This can be equal: quantities, sets, expressions, or anything else that can be described as an element.
Set A is equal to set B iff (if and only if) all of the members of set A match those of set B (without any extra or excluded elements).
Set A does not equal set B if any of the members contained in either set do not match a member contained in the other set.
Describes an empty set, or a set with no members.
The act of merging all of the elements between sets together. (Be careful not to repeat elements in the resulting set)
The act of combining only the common elements between sets together.
Set A is a subset of set B iff set B contains every element contained within set A and at least one more element in which set A does not.
As with the plain subset, A is a subset of B iff every element of A is a member of set B; however, contrary to the plain subset, set A may equal set B.
The size of a set, or the number of members contained within a set.
Represents the action of adding together the elements of set A with those of set B in a distributive fashion. This is done by taking each member from set A and summing it with every member in set B, with each sum being a member in the resulting set.
The relative complement, or difference operation refers to the action of subtracting (or getting rid of) every member from set A that is also a member of set B.
This difference operation results in a set that includes all members of sets A and B excluding elements common to both sets.
The power set operation results in a set that contains every combination of elements from a set, including mixed combinations and the null set.
The universal set is the set which contains all elements considered during set operations. This does not only contain elements which are a member of a designated set but all possible elements that may be a member of a given set.
The complement of a set is its opposite, or all of the elements the set does not have. The complement of set A is the universal set U minus set A: A'=U-A.
The domain of a set describes all of the elements it has as its members. Set notation is how the domain is notated and described.
A set which has every real number in existence as its members. Entities that are members of this set are called 'real numbers,' and it is with these elements that mathematics is formed.
A set which includes all numbers which are not rational. These numbers are called 'irrational' and they include numbers with an infinitely non-repeating fractional part or with an imaginary component (i).
Any number that can be broken down into a ratio of two integers is called 'rational'. This includes all numbers with terminating, or repeating fractional components.
A set containing all the real numbers (positive and negative) without fractional components.
A set containing all integers that are greater than or equal to zero.
A set containing all integers that are greater than but not equal to zero.
A set containing all numbers with an imaginary component (i).
- Robert R. Stroll (1963)
Publisher: W. H. Freeman
Call Number: QA248 .S7985
ISBN-13: 9780486638294
- Robert R. Stroll (1974)
Publisher: W.H. Freeman
Call Number: QA248.3 .S78
ISBN-10: 0716704579
- Paul R. Halmos (2017)
Publisher: Dover
Call Number: QA248 .H26
ISBN-13: 9780486814872
- Norman T. Hamilton, Joseph Landin (2018)
Publisher: Dover
Call Number: QA248 .H28
ISBN-13: 9780486824727
- Granino Korn, Theresa Korn (1968)
Publisher: Dover
Call Number: QA40 .K598
ISBN-10: 0486411478
- Robert Blitzer (2010)
Publisher: Pearson
Call Number: QA154.3 .B586
ISBN-13: 9780321559845
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