Addition and Set theory

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Difference between Addition and Set theory

Addition vs. Set theory

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division. Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

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Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.

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Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

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Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

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Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

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Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Ordinal number

In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Richard Dedekind

Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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