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In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. [5] A set may have a finite number of elements or be an infinite set.
- Mathematical Object
Schlegel wireframe 8-cell. A mathematical object is an...
- Element (Mathematics)
Suppes, Patrick (1972) [1960], Axiomatic Set Theory, NY:...
- Infinite Set
The set of all even integers is also a countably infinite...
- Language
Language of mathematics. The language of mathematics or...
- Mathematical Object
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
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A set is an idea from mathematics. A set has members (also called elements ). A set is defined by its members, so any two sets with the same members are the same (e.g., if set and set have the same members, then ). Example of a set of polygons. A set cannot have the same member more than once.
In sets it does not matter what order the elements are in. Example: {1,2,3,4} is the same set as {3,1,4,2} When we say order in sets we mean the size of the set. Another (better) name for this is cardinality. A finite set has finite order (or cardinality). An infinite set has infinite order (or cardinality).
Set theory. A Venn diagram illustrating the intersection of two sets. Set theory is the study of sets in mathematics. Sets are collections of objects. We refer to these objects as "elements" or "members" of the set. To write a set, one wraps the numbers in {curly brackets}, and separates them with commas. For example. the set holds 1, 2, and 3.
Equality of Sets. Two sets A and B are said to be equal if they contain the same collection of elements. More rigorously, we define A = B ⇔ ∀x(x ∈ A ⇔ x ∈ B). Since the elements of a set can themselves be sets, exercise caution and use proper notation when you compare the contents of two sets.
