Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.

Philadelphia

Philadelphia (/ˌfɪləˈdɛlfiə/) is the largest city in the Commonwealth of Pennsylvania and the fifth-most-populous in the United States, with an estimated population in 2014 of 1,560,297. In the Northeastern United States, at the confluence of the Delaware and Schuylkill River, Philadelphia is the economic and cultural anchor of the Delaware Valley, a metropolitan area home to 7.2 million people and the eighth-largest combined statistical area in the United States.

In 1682, William Penn founded the city to serve as capital of the Pennsylvania Colony. Philadelphia played an instrumental role in the American Revolution as a meeting place for the Founding Fathers of the United States, who signed the Declaration of Independence in 1776 and the Constitution in 1787. Philadelphia was one of the nation's capitals in the Revolutionary War, and served as temporary U.S. capital while Washington, D.C., was under construction. In the 19th century, Philadelphia became a major industrial center and railroad hub that grew from an influx of European immigrants. It became a prime destination for African-Americans in the Great Migration and surpassed two million occupants by 1950.

Capital City

Capital City or Capitol City or variants, may refer to :

Capital city

Capital cities

Capitol city

Big Bang

The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution. The model accounts for the fact that the universe expanded from a very high density and high temperature state, and offers a comprehensive explanation for a broad range of phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure and Hubble's Law. If the known laws of physics are extrapolated beyond where they are valid, there is a singularity. Modern measurements place this moment at approximately 13.8 billion years ago, which is thus considered the age of the universe. After the initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later simple atoms. Giant clouds of these primordial elements later coalesced through gravity to form stars and galaxies.

A Tribe Called Quest

A Tribe Called Quest was an American hip hop group that was formed in 1985, and was composed of MC/producer Q-Tip, MC Phife Dawg aka Phife Diggy (Malik Taylor), and DJ/producer Ali Shaheed Muhammad. A fourth member, rapper Jarobi White, left the group after their first album in 1991. He continued to contribute to the band sporadically before rejoining for their 2006 reunion. Along with De La Soul, the group was a central part of the Native Tongues Posse, and enjoyed the most commercial success out of all the groups to emerge from that collective. Many of their songs, such as "Bonita Applebum", "Can I Kick It?", "I Left My Wallet in El Segundo", "Scenario", "Check the Rhime", "Jazz (We've Got)", "Award Tour" and "Electric Relaxation" are regarded as classics. The group released five albums between 1990 and 1998 and disbanded in 1998. In 2006, the group reunited and toured the US. The group is regarded as pioneers of alternative hip hop music, having helped to pave the way for many innovative artists.