Before the featured portal process ceased in 2017, this had been designated as a featured portal.

Portal:Mathematics

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

The Mathematics Portal


Mathematics is the study of numbers, quantity, space, pattern, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.

Refresh with new selections below (purge)

Selected article

A number is an abstract entity that represents a count or measurement. A symbol for a number is called a numeral. The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.

Numbers can be classified into sets called number systems. The most familiar numbers are the natural numbers, which to some mean the non-negative integers and to others mean the positive integers. In everyday parlance the non-negative integers are commonly referred to as whole numbers, the positive integers as counting numbers, symbolised by . Mathematics is used in many classes throughout the course of one's education.

The integers consist of the natural numbers (positive whole numbers and zero) combined with the negative whole numbers, which are symbolised by (from the German Zahl, meaning "number").

A rational number is a number that can be expressed as a fraction with an integer numerator and a non-zero natural number denominator. Fractions can be positive, negative, or zero. The set of all fractions includes the integers, since every integer can be written as a fraction with denominator 1. The symbol for the rational numbers is a bold face (for quotient).

View all selected articles Read More...

Selected image

spiral figure representing both finite and transfinite ordinal numbers

This spiral diagram represents all ordinal numbers less than ωω. The first (outermost) turn of the spiral represents the finite ordinal numbers, which are the regular counting numbers starting with zero. As the spiral completes its first turn (at the top of the diagram), the ordinal numbers approach infinity, or more precisely ω, the first transfinite ordinal number (identified with the set of all counting numbers, a "countably infinite" set, the cardinality of which corresponds to the first transfinite cardinal number, called 0). The ordinal numbers continue from this point in the second turn of the spiral with ω + 1, ω + 2, and so forth. (A special ordinal arithmetic is defined to give meaning to these expressions, since the + symbol here does not represent the addition of two real numbers.) Halfway through the second turn of the spiral (at the bottom) the numbers approach ω + ω, or ω · 2. The ordinal numbers continue with ω · 2 + 1 through ω · 2 + ω = ω · 3 (three-quarters of the way through the second turn, or at the "9 o'clock" position), then through ω · 4, and so forth, up to ω · ω = ω2 at the top. (As with addition, the multiplication and exponentiation operations have definitions that work with transfinite numbers.) The ordinals continue in the third turn of the spiral with ω2 + 1 through ω2 + ω, then through ω2 + ω2 = ω2 · 2, up to ω2 · ω = ω3 at the top of the third turn. Continuing in this way, the ordinals increase by one power of ω for each turn of the spiral, approaching ωω in the middle of the diagram, as the spiral makes a countably infinite number of turns. This process can actually continue (not shown in this diagram) through and , and so on, approaching the first epsilon number, ε0. Each of these ordinals is still countable, and therefore equal in cardinality to ω. After uncountably many of these transfinite ordinals, the first uncountable ordinal is reached, corresponding to only the second infinite cardinal . The identification of this larger cardinality with the cardinality of the set of real numbers can neither be proved nor disproved within the standard version of axiomatic set theory called Zermelo–Fraenkel set theory, whether or not one also assumes the axiom of choice.

Did you know…

Did you know...

                         

Showing 7 items out of 75

WikiProjects

The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.

WikiProjects

Project pages

Essays

Subprojects

Related projects

Things you can do

Subcategories


Topics in mathematics

General Foundations Number theory Discrete mathematics
Nuvola apps bookcase.svg
Set theory icon.svg
Nuvola apps kwin4.png
Nuvola apps atlantik.png


Algebra Analysis Geometry and topology Applied mathematics
Arithmetic symbols.svg
Source
Nuvola apps kpovmodeler.svg
Gcalctool.svg

Index of mathematics articles

ARTICLE INDEX: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (0–9)
MATHEMATICIANS: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Related portals

Portal:Algebra Portal:Arithmetic Portal:Category theory Portal:Computer science Portal:Cryptography Portal:Discrete mathematics Portal:Geometry
Algebra Arithmetic Category
theory
Computer
science
Cryptography Discrete
mathematics
Geometry
Portal:Logic Portal:Mathematical analysis Portal:Mathematics Portal:Number theory Portal:Physics Portal:Science Portal:Set theory Portal:Statistics Portal:Topology
Logic Mathematical analysis Mathematics Number
theory
Physics Science Set theory Statistics Topology


In other Wikimedia projects

The following Wikimedia Foundation sister projects provide more on this subject:

Wikibooks
Books

Commons
Media

Wikinews 
News

Wikiquote 
Quotations

Wikisource 
Texts

Wikiversity
Learning resources

Wiktionary 
Definitions

Wikidata 
Database

Retrieved from "https://en.wikipedia.org/w/index.php?title=Portal:Mathematics&oldid=895914657"
This content was retrieved from Wikipedia : http://en.wikipedia.org/wiki/Portal:Mathematics
This page is based on the copyrighted Wikipedia article "Portal:Mathematics"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA