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.

Underwater diving

Underwater diving is the practice of going underwater, either with breathing apparatus (scuba diving and surface supplied diving) or by breath-holding (freediving). Atmospheric diving suits may be used to isolate the diver from the effects of high ambient pressure, or the saturation diving technique can be used to reduce the risk of decompression sickness after deep dives.

Diving activities are restricted to relatively shallow depths, as even armored atmospheric diving suits are unable to withstand the pressures of the deeper waters of the world. Diving is also restricted to conditions which are not excessively hazardous, though the level of risk acceptable to the diver can vary considerably. Occasionally divers may dive in liquids other than water.

The term deep sea diving refers to underwater diving, usually with surface supplied equipment, and often refers specifically to the use of standard diving dress with the traditional copper helmet. Hard hat diving is any form of diving with a helmet, including the standard copper helmet, other forms of free-flow helmet and lightweight demand helmets.

Deep

Deep or The Deep may refer to:

Places

Film and television

Sea

A sea is a large body of salt water that is surrounded in whole or in part by land. More broadly, "the sea" is the interconnected system of Earth's salty, oceanic waters—considered as one global ocean or as several principal oceanic divisions. The sea moderates Earth's climate and has important roles in the water cycle, carbon cycle, and nitrogen cycle. Although the sea has been travelled and explored since prehistory, the modern scientific study of the sea—oceanography—dates broadly to the British Challenger expedition of the 1870s. The sea is conventionally divided into up to five large oceanic sections—including the IHO's four named oceans (the Atlantic, Pacific, Indian, and Arctic) and the Southern Ocean; smaller, second-order sections, such as the Mediterranean, are known as seas.

Owing to the present state of continental drift, the Northern Hemisphere is now fairly equally divided between land and sea (a ratio of about 2:3) but the South is overwhelmingly oceanic (1:4.7).Salinity in the open ocean is generally in a narrow band around 3.5% by mass, although this can vary in more landlocked waters, near the mouths of large rivers, or at great depths. About 85% of the solids in the open sea are sodium chloride. Deep-sea currents are produced by differences in salinity and temperature. Surface currents are formed by the friction of waves produced by the wind and by tides, the changes in local sea level produced by the gravity of the Moon and Sun. The direction of all of these is governed by surface and submarine land masses and by the rotation of the Earth (the Coriolis effect).

Galaxy

A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. The word galaxy is derived from the Greek galaxias (γαλαξίας), literally "milky", a reference to the Milky Way. Galaxies range in size from dwarfs with just a few thousand (10³) stars to giants with one hundred trillion (10¹⁴) stars, each orbiting their galaxy's own center of mass. Galaxies, are categorized according to their visual morphology, including elliptical,spiral, and irregular. Many galaxies are thought to have black holes at their active centers. The Milky Way's central black hole, known as Sagittarius A*, has a mass four million times greater than the Sun. As of July 2015, EGSY8p7 is the oldest and most distant observed galaxy with a light travel distance of 13.2 billion light-years from Earth, and observed as it existed 570 million years after the Big Bang. Previously, as of May 2015, EGS-zs8-1 was the most distant known galaxy, estimated to have a light travel distance of 13.1 billion light-years away and to have 15% of the mass of the Milky Way.