Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing and includes the theory of computation.
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproven statement that is believed true is known as a conjecture.
Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.
Phoenix (// FEE-niks; O'odham: S-ki:kigk; Yavapai: Wathinka or Wakatehe; Western Apache: Fiinigis; Navajo: Hoozdoh; Mojave: Hachpa 'Anya Nyava) is the capital, and largest city, of the U.S. state of Arizona, as well as the sixth most populous city nationally, after (in order) New York, Los Angeles, Chicago, Houston, and Philadelphia. Phoenix is also the most populous state capital in the United States. Phoenix is home to 1,445,632 people according to the 2010 U.S. Census Bureau data.
It is the anchor of the Phoenix metropolitan area (also known as the Valley of the Sun) and is the 12th largest metro area by population in the United States with about 4.2 million people in 2010. In addition, Phoenix is the county seat of Maricopa County and is one of the largest cities in the United States by land area.
In journalism, a human interest story is a feature story that discusses a person or people in an emotional way. It presents people and their problems, concerns, or achievements in a way that brings about interest, sympathy or motivation in the reader or viewer.
Human interest stories may be "the story behind the story" about an event, organization, or otherwise faceless historical happening, such as about the life of an individual soldier during wartime, an interview with a survivor of a natural disaster, a random act of kindness or profile of someone known for a career achievement.
The term crime does not, in modern times, have any simple and universally accepted definition, but one definition is that a crime, also called an offence or a criminal offence, is an act harmful not only to some individual, but also to the community or the state (a public wrong). Such acts are forbidden and punishable by law.
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite (TCP/IP) to serve several billion users worldwide. It is a network of networks that consists of millions of private, public, academic, business, and government networks, of local to global scope, that are linked by a broad array of electronic, wireless and optical networking technologies. The Internet carries an extensive range of information resources and services, such as the inter-linked hypertext documents of the World Wide Web (WWW), the infrastructure to support email, and peer-to-peer networks.
Most traditional communications media including telephone, music, film, and television are being reshaped or redefined by the Internet, giving birth to new services such as voice over Internet Protocol (VoIP) and Internet Protocol television (IPTV). Newspaper, book and other print publishing are adapting to website technology, or are reshaped into blogging and web feeds. The Internet has enabled and accelerated new forms of human interactions through instant messaging, Internet forums, and social networking. Online shopping has boomed both for major retail outlets and small artisans and traders. Business-to-business and financial services on the Internet affect supply chains across entire industries.
The United States of America (USA), commonly referred to as the United States (US), America, or simply the States, is a federal republic consisting of 50 states, 16 territories, and a federal district. The 48 contiguous states and the federal district of Washington, D.C., are in central North America between Canada and Mexico. The state of Alaska is the northwestern part of North America and the state of Hawaii is an archipelago in the mid-Pacific. The country also has five populated and nine unpopulated territories in the Pacific and the Caribbean. The largest of these territories are Puerto Rico and the American Virgin Islands which are an official part of the United States. At 3.79 million square miles (9.83 million km2) in total and with around 316 million people, the United States is the fourth-largest country by total area and third largest by population. It is one of the world's most ethnically diverse and multicultural nations, the product of large-scale immigration from many countries. The geography and climate of the United States is also extremely diverse, and it is home to a wide variety of wildlife.
Paleo-indians migrated from Asia to what is now the U.S. mainland around 15,000 years ago, with European colonization beginning in the 16th century. The United States emerged from 13 British colonies located along the Atlantic seaboard. Disputes between Great Britain and these colonies led to the American Revolution. On July 4, 1776, delegates from the 13 colonies unanimously issued the Declaration of Independence. The ensuing war ended in 1783 with the recognition of independence of the United States from the Kingdom of Great Britain, and was the first successful war of independence against a European colonial empire. The current Constitution was adopted on September 17, 1787. The first 10 amendments, collectively named the Bill of Rights, were ratified in 1791 and guarantee many fundamental civil rights and freedoms.