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Complex number and Rational number

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Complex number and Rational number

Complex number vs. Rational number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation. In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

Similarities between Complex number and Rational number

Complex number and Rational number have 29 things in common (in Unionpedia): Addition, Additive inverse, Algebraic closure, Algebraic number, Algebraic number field, Blackboard bold, Characteristic (algebra), Coefficient, E (mathematical constant), Field (mathematics), Field extension, Fraction (mathematics), If and only if, Locally compact space, Mathematical analysis, Matrix (mathematics), Metric space, Multiplicative inverse, Number, Ordered pair, Ostrowski's theorem, P-adic number, Pi, Prime number, Real number, Set (mathematics), Square root of 2, Topological ring, Total order.

Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

Addition and Complex number · Addition and Rational number · See more »

Additive inverse

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

Additive inverse and Complex number · Additive inverse and Rational number · See more »

Algebraic closure

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.

Algebraic closure and Complex number · Algebraic closure and Rational number · See more »

Algebraic number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

Algebraic number and Complex number · Algebraic number and Rational number · See more »

Algebraic number field

In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.

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Blackboard bold

Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled.

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Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.

Characteristic (algebra) and Complex number · Characteristic (algebra) and Rational number · See more »

Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

Coefficient and Complex number · Coefficient and Rational number · See more »

E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

Complex number and E (mathematical constant) · E (mathematical constant) and Rational number · See more »

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

Complex number and Field (mathematics) · Field (mathematics) and Rational number · See more »

Field extension

In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.

Complex number and Field extension · Field extension and Rational number · See more »

Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

Complex number and Fraction (mathematics) · Fraction (mathematics) and Rational number · See more »

If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

Complex number and If and only if · If and only if and Rational number · See more »

Locally compact space

In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.

Complex number and Locally compact space · Locally compact space and Rational number · See more »

Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

Complex number and Mathematical analysis · Mathematical analysis and Rational number · See more »

Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Complex number and Matrix (mathematics) · Matrix (mathematics) and Rational number · See more »

Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

Complex number and Metric space · Metric space and Rational number · See more »

Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

Complex number and Multiplicative inverse · Multiplicative inverse and Rational number · See more »

Number

A number is a mathematical object used to count, measure and also label.

Complex number and Number · Number and Rational number · See more »

Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

Complex number and Ordered pair · Ordered pair and Rational number · See more »

Ostrowski's theorem

In number theory, Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers Q is equivalent to either the usual real absolute value or a p-adic absolute value.

Complex number and Ostrowski's theorem · Ostrowski's theorem and Rational number · See more »

P-adic number

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

Complex number and P-adic number · P-adic number and Rational number · See more »

Pi

The number is a mathematical constant.

Complex number and Pi · Pi and Rational number · See more »

Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Complex number and Prime number · Prime number and Rational number · See more »

Real number

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

Complex number and Real number · Rational number and Real number · See more »

Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

Complex number and Set (mathematics) · Rational number and Set (mathematics) · See more »

Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.

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Topological ring

In mathematics, a topological ring is a ring R which is also a topological space such that both the addition and the multiplication are continuous as maps where R × R carries the product topology.

Complex number and Topological ring · Rational number and Topological ring · See more »

Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.

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The list above answers the following questions

Complex number and Rational number Comparison

Complex number has 295 relations, while Rational number has 93. As they have in common 29, the Jaccard index is 7.47% = 29 / (295 + 93).

References

This article shows the relationship between Complex number and Rational number. To access each article from which the information was extracted, please visit:

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