সংখ্যাৰ প্ৰকাৰসমূহৰ তালিকা

এটি ইউলাৰ চিত্ৰত প্ৰকৃত সংখ্যাৰ কেইটামান প্ৰকাৰক দেখুওৱা হৈছে

Numbers can be classified according to how they are represented or according to the properties that they have.

মুখ্য প্ৰকাৰসমূহ

স্বাভাবিক সংখ্যাs 

The counting numbers {1, 2, 3, ...}, sometimes including zero.

অখণ্ড সংখ্যাs 

Positive and negative counting numbers, as well as zero.

বাস্তব সংখ্যাs 

Numbers that can be expressed as a fraction of two integers.

প্ৰাকৃতিক সংখ্যাs 

All numbers that can be expressed as the limit of a sequence of rational numbers. Every real number corresponds to a point on the number line.

অবাস্তব সংখ্যাs 

A real number that is not rational is called irrational or transcendental.

জটিল সংখ্যাs 

Includes real numbers and imaginary numbers, such as the square root of negative one.

Number representations

Decimal 

The standard Hindu–Arabic numeral system using base ten.

Binary 

The base-two numeral system used by computers. See positional notation for information on other bases.

Roman numerals 

The numeral system of ancient Rome, still occasionally used today.

Fractions

A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers.

Scientific notation

A method for writing very small and very large numbers using powers of ten. When used in science, such a number also conveys the precision of measurement using significant figures.

Knuth's up-arrow notation and Conway chained arrow notation

Notations that allow the concise representation of extremely large integers such as Graham's number.

Signed numbers

Positive numbers 

Real numbers that are greater than zero.

Negative numbers 

Real numbers that are less than zero.

Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used:

Non-negative numbers 

Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero or positive.

Non-positive numbers 

Real numbers that are less than or equal to zero. Thus a non-positive number is either zero or negative.

Types of integers

Even and odd numbers 

A number is even if it is a multiple of two, and is odd otherwise.

Prime number 

A number with exactly two positive divisors.

Composite number 

A number that can be factored into a product of smaller integers. Every integer greater than one is either prime or composite.

Square number 

A numbers that can be written as the square of an integer.

There are many other famous integer sequences, such as the sequence of Fibonacci numbers, the sequence of factorials, the sequence of perfect numbers, and so forth.

Algebraic numbers

Algebraic number 

Any number that is the root of a non-zero polynomial with rational coefficients.

Transcendental number 

Any real or complex number that is not algebraic. Examples include e and π.

Quadratic surd 

An algebraic number that is the root of a quadratic equation. Such a number can be expressed as the sum of a rational number and the square root of a rational.

Constructible number 

A number representing a length that can be constructed using a compass and straightedge. These are a subset of the algebraic numbers, and include the quadratic surds.

Algebraic integer 

An algebraic number that is the root of a monic polynomial with integer coefficients.

Non-standard numbers

Transfinite numbers 

Numbers that are greater than any natural number.

Ordinal numbers 

Infinite numbers used to describe the order types of well-ordered sets. These include thecardinal numbers, which are used to describe the cardinalities of sets.

Infinitesimals 

Reciprocals of infinite numbers. These are smaller than any positive real number, but are nonetheless greater than zero. These were used extensively in the initial development of calculus.

Hyperreal numbers 

The numbers used in non-standard analysis. These include infinite and infinitesimal numbers which possess certain properties of the real numbers.

Surreal numbers 

A number system that includes the hyperreal numbers as well as the ordinals. The surreal numbers are the largest possible ordered field.

Computability and definability

Computable number 

A real number whose digits can be computed using an algorithm.

Definable number 

A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory.