click links in text for more info

Mathematical proof

A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other established statements, such as theorems. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. An unproven proposition, believed to be true is known as a conjecture, or a hypothesis if used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language which admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written in symbolic language without the involvement 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, so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures. The philosophy of mathematics is concerned with the role of language and logic in proofs, mathematics as a language; the word "proof" comes from the Latin probare. Related modern words are English "probe", "probation", "probability", Spanish probar, Italian provare, German probieren; the legal term "probity" means authority or credibility, the power of testimony to prove facts when given by persons of reputation or status. Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof, it is that the idea of demonstrating a conclusion first arose in connection with geometry, which originated in practical problems of land measurement. The development of mathematical proof is the product of ancient Greek mathematics, one of its greatest achievements.

Thales and Hippocrates of Chios gave some of the first known proofs of theorems in geometry. Eudoxus and Theaetetus formulated did not prove them. Aristotle said definitions should describe the concept being defined in terms of other concepts known. Mathematical proof was revolutionized by Euclid, who introduced the axiomatic method still in use today, it starts with undefined terms and axioms, propositions concerning the undefined terms which are assumed to be self-evidently true. From this basis, the method proves theorems using deductive logic. Euclid's book, the Elements, was read by anyone, considered educated in the West until the middle of the 20th century. In addition to theorems of geometry, such as the Pythagorean theorem, the Elements covers number theory, including a proof that the square root of two is irrational and a proof that there are infinitely many prime numbers. Further advances took place in medieval Islamic mathematics. While earlier Greek proofs were geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs with no dependence on geometric intuition.

In the 10th century CE, the Iraqi mathematician Al-Hashimi worked with numbers as such, called "lines" but not considered as measurements of geometric objects, to prove algebraic propositions concerning multiplication, etc. including the existence of irrational numbers. An inductive proof for arithmetic sequences was introduced in the Al-Fakhri by Al-Karaji, who used it to prove the binomial theorem and properties of Pascal's triangle. Alhazen developed the method of proof by contradiction, as the first attempt at proving the Euclidean parallel postulate. Modern proof theory treats proofs as inductively defined data structures, not requiring an assumption that axioms are "true" in any sense; this allows parallel mathematical theories as formal models of a given intuitive concept, based on alternate sets of axioms, for example Axiomatic set theory and Non-Euclidean geometry. As practiced, a proof is expressed in natural language and is a rigorous argument intended to convince the audience of the truth of a statement.

The standard of rigor has varied throughout history. A proof can be presented differently depending on the intended audience. In order to gain acceptance, a proof has to meet communal standards of rigor; the concept of proof is formalized in the field of mathematical logic. A formal proof is written in a formal language instead of a natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, with each subsequent formula a logical consequence of the preceding ones; this definition makes the concept of proof amenable to study. Indeed, the field of proof theory studies formal proofs and their properties, the most famous and surprising being that all axiomatic systems can generate certain undecidable statements not provable within the system; the definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof.

However, outside the

Lumír Ondřej Hanuš

Lumír Ondřej Hanuš is a Czech analytic chemist and leading authority in the field of cannabis research. In 1992, he and William Anthony Devane isolated and first described the structure of anandamide, an endogenous cannabinoid neurotransmitter. Lumír Hanuš was born in 1947 in Olomouc, in what was Czechoslovakia, he is a distant relative of Czech chemist Josef Hanuš. In 1966, Hanuš began studying at the Faculty of Science of Palacký University Olomouc. In 1970, professor Zdeněk Krejčí of the Faculty of Medicine's Department of Hygiene and Epidemiology needed an aide. Hanuš started to work as Krejčí's assistant in the research of cannabis and hashish in December of that year. There, Hanuš met professors Jan Kabelík and František Šantavý, together with Krejčí, laid the foundations of the research of cannabis and its curative effects. Hanuš grew cannabis for research purposes on two fields in the Research Institute of Vegetable Growing and Breeding in Olomouc from 1971; the extracts were used at the University Hospital Olomouc as a cure for aphthous ulcer, herpes simplex, herpes zoster, pressure ulcers.

Hanuš graduated with a Master of Science in 1972 and he earned a Doctorate in Science at Olomouc in 1974. He pursued his academic and research activities there until 1990. Hanuš took part in research at the Czechoslovak Academy of Sciences and continued post-graduate research study at Jan Evangelista Purkyně University in Brno. In years 1978–1979 he worked as a research associate at the University of Mississippi, focusing not only on cannabis, but on coca leaves, he became associate professor in organic chemistry in Olomouc in 1994 and obtained a Doctorate of Sciences in pharmaceutical chemistry at Charles University in 1995. Hanuš was for many years in contact with Israeli cannabis researcher Raphael Mechoulam by letter. Following the Velvet Revolution, Hanuš was invited to continue his research at Hebrew University of Jerusalem in Israel. In Israel, Hanuš and American molecular pharmacologist William Anthony Devane in 1992 first described the structure of Anandamide, an endogenous cannabinoid neurotransmitter.

Hanuš continues his research in Jerusalem on cannabinoids and their derivatives. Hanuš marks cannabis as "one of the safest known medications". According to Hanuš, alcohol and tobacco should be "blacklisted" rather than cannabis, as there is a possibility of both physical and psychological addiction to the first two, while there is no possibility of physical, only limited possibility of psychological addiction to marijuana. Moreover, people under the influence of marijuana are not dangerous to others, he does not support smoking marijuana because of the dangers of smoke inhalation. Hanuš is against uncontrolled use of marijuana, but he supports its use for medical purposes. In April 2010 and September 2011, Hanuš took part in a seminar of the Czech Parliament aimed at introduction of cannabinoid treatment. September 14, 2005: Hanuš Medal for furthering creditable work in the fields of chemistry. November 6, 2006: Memorial Medal on the 50th anniversary of the revival and reopening of the university in Olomouc at the occasion of delivering the 13th annual lecture in honour of J. L. Fischer April 12, 2007: Doctor honoris causa 2009: nominated for the National Award of the Czech Government "Czech Mind" 2010: nominated for the Patria Award of the Czech Government "Czech Mind" 2010: nominated for The 2010 Jack Herer Award for Outstanding Hemp Awareness in the field of Medicine April 26, 2010: Outstanding Immigrant Scientist for his contribution to the State of Israel, Ministry of Immigrant Absorption, Israel May 4, 2011: Doctor honoris causa 2011: Honorary Scientific Fellow of the Czech Neuropsychopharmacological Society 2011: nominated for the Addictology award for best achievement in the year 2011 November 22, 2012: Addictology Award for significant contribution in the field of addictology in the past year June 13, 2013: Olomouc City Award for the year 2012 Anandamide 2-Arachidonyl glyceryl ether Medical cannabis Dr. Lumir Hanus, Hebrew University of Jerusalem – Faculty of Medicine A poem performed by Lumír Hanuš on YouTube in Moravian dialect

Glenn Hubbard (baseball)

Glenn Dee Hubbard is a former first base coach for the Atlanta Braves and second baseman in Major League Baseball who played from 1978 to 1989. Hubbard played his first ten seasons with the Atlanta Braves and his last two with the Oakland Athletics. Glenn Hubbard attended Wheatland High School, just outside Beale AFB, CA, where his father was stationed, he finished high school at Ben Lomond High School when his father moved to Hill Air Force Base near Ogden, Utah. Out of high school, he was a 20th round selection in the 1975 MLB draft and was promoted to the major leagues in 1978. Hubbard hit his first major league home run on September 23, 1978. Hubbard's career with the Braves lasted from 1978 to 1987. Hubbard signed as a free agent with the Oakland Athletics and played with them in 1988 and 1989. In 1983, Hubbard had his best season. During his 7th inning at-bat, announcers Vin Scully and Joe Garagiola made numerous light-hearted comments about his full beard, as beards were not in fashion at the time.

Hubbard got a single when he hit a hard grounder to Cal Ripken. The ball took a wicked hop. Hubbard was known more for his fielding than his hitting, his willingness to stand in while turning a double play with a runner coming at him and his steady glove made him valuable for the Braves. He holds Braves' team fielding records for second basemen in all categories, he was an excellent bunter and in 1982 he led the National League in sacrifice hits. Hubbard's most notable trading card is the 1984 Fleer version in which he has an eight-foot boa constrictor draped around his neck. Hubbard was the Braves' first base coach from 1999 to 2010 under manager Bobby Cox; when Fredi Gonzalez was hired as the Braves manager on October 13, 2010, Hubbard was not offered a position on his staff. The previous hitting coach, Terry Pendleton, replaced him; the Kansas City Royals organization hired Hubbard in 2011. As of the 2015 season Hubbard is now bench coach for the Lexington Legends who operate as the Royals class A team.

On June 24, 2016, the Legends held a promotional giveaway with a Glenn Hubbard bobblehead featuring him in a Legends uniform with a boa constrictor draped across his neck, an image made popular by his 1984 Fleer baseball card. Career statistics and player information from MLB, or ESPN, or Baseball-Reference, or Fangraphs, or Baseball-Reference, or Retrosheet, or Pelota Binaria

Pennsylvania Route 741

Pennsylvania Route 741 is a 26.3-mile-long state highway that runs through western and southern Lancaster County in the U. S. state of Pennsylvania. The western terminus is along Rohrerstown Road north of an intersection with Commercial Avenue near East Petersburg; the eastern terminus is at PA 41 in Gap. PA 741 runs through the western suburbs of Lancaster; the route passes through Millersville before it turns east at New Danville. PA 741 forms a concurrency with U. S. Route 222 between Willow Street and Lampeter before it continues east through farmland in the Pennsylvania Dutch Country, home to several Amish families, passing through Strasburg before reaching Gap; the section of road between Willow Street and Lampeter was designated as part of US 230 in 1926 and concurrent with PA 72 in 1927, with US 222 replacing US 230 by 1928. In 1928, the road between Willow Street and Gap became part of PA 41. PA 741 was designated by 1930 to run from PA 41 north to US 30 in Gap. In the 1930s, PA 41 and PA 741 switched alignments, with PA 741 running between US 222 in Lampeter and PA 41 in Gap and PA 41 heading north to US 30.

PA 741 was extended west to PA 324 south of New Danville in the 1970s. The route was extended west to PA 722 in East Petersburg in the 1980s; the western terminus was cut to its current location after 2005. PA 741 begins at an arbitrary point along Rohrerstown Road north of an intersection with Commercial Avenue in East Hempfield Township in Lancaster County, with Rohrerstown Road continuing north towards the borough of East Petersburg past the terminus of PA 741. From this point, PA 741 heads south as a three-lane road with a center left-turn lane, locally-maintained, passing through industrial parks; the route continues to an interchange with PA 283. The road crosses the Little Conestoga Creek into Manheim Township after PA 283; the route becomes two lanes again and turns east prior to turning southwest and crossing the Little Conestoga Creek back into East Hempfield Township. At this point, PA 741 becomes McGovernville Road and comes to a bridge over Norfolk Southern's Lititz Secondary and Amtrak's Keystone Corridor.

The road passes a mix of homes and woods as it comes to the Harrisburg Pike intersection, where it makes a turn to the south onto Rohrerstown Road, a three lane road with a center left-turn lane. PA 741 passes homes to the west and a branch of Lancaster General Hospital to the east prior to coming to the US 30 interchange. In the area of the interchange, PA 741 is a divided highway. Following US 30, the route becomes a two-lane undivided road and passes residences prior to crossing Norfolk Southern's Columbia Secondary at-grade and entering the residential and commercial community of Rohrerstown. Here, PA 741 crosses PA 23. After leaving Rohrerstown, the road passes a mix of farms and businesses prior to an intersection with PA 462. After this intersection, PA 741 enters Manor Township and becomes Millersville Road, passing farm fields to the west and suburban residential neighborhoods to the east. Farther south, the road enters areas of woods and homes, making a turn to the southeast and crossing Little Conestoga Creek.

The road forms the border between Manor Township to the southwest and the borough of Millersville to the northeast prior to entering Millersville and crossing PA 999, at which point the road passes businesses. Following this intersection, PA 741 heads through farmland before passing a few homes. At the Wabank Road intersection, the road enters Lancaster Township and passes a mix of homes and farms before crossing the Conestoga River. At this point, PA 741 continues into Pequea Township and runs through agricultural areas prior to entering the residential community of New Danville. Here, the route intersects PA 324 and forms a concurrency with that route, heading south on Marticville Road out of New Danville. PA 741 splits from PA 324 by turning east onto Long Lane, passing more farmland and crossing into West Lampeter Township. Upon reaching the community of Willow Street, PA 741 widens into a two-lane divided highway and meets the southbound direction of US 222/PA 272. Here, the route enters commercial areas.

A short distance the road intersects the northbound direction of US 222/PA 272, at which point PA 741 becomes concurrent with both directions of US 222. The two routes continue east on Beaver Valley Pike, passing farms to the north and commercial development to the south; the road becomes undivided and passes agricultural areas and homes before PA 741 splits from US 222 by continuing east on Village Road. At this point, the route enters the Pennsylvania Dutch Country of eastern Lancaster County, home to many Amish farms; the route continues through a mix of farms and residences as it passes the community of Lampeter, where it passes south of Lampeter-Strasburg High School. After crossing the Pequea Creek, PA 741 turns to the southeast. Upon crossing into the borough of Strasburg, the route heads east-northeast onto Miller Street and passes several homes. At the Strasburg Pike intersection, PA 741 heads east onto West Main Street and comes to the center of Strasburg at Decatur Street; the route continue past more homes on East Main Street prior to crossing into Strasburg Township and meeting PA 896.

At this point, PA 741 continues east on Gap Road between farms to the north and residential and commercial development to the south, passing north of the Choo Choo Barn. The route crosses the Strasburg Rail Road at-grade and passes between the East Strasburg station along the Strasburg Rail Road to the north and the Railroad Museum of Pennsylvania to the south; the road continues into open fa

Alli Mia Fora (Antique album)

Alli Mia Fora is the final album by Greek musical group Antique. The album was released in November 2002 by V2 Records and it became gold in Greece, their first album to do so. In 2003, many of the songs from this album were included in English on their Swedish release titled Blue Love. "Alli Mia Fora" The first single from the album was "Alli Mia Fora". The music video was directed by Kostas Kapetanidis, it was released as an English version called "Time to Say Goodbye" on their follow-up album Blue Love"Moro Mou" The second single from the album was "Moro Mou". A mixed Greek and English version was released from Blue Love called "Moro Mou". Lyrics

Melmont, Washington

Melmont is a ghost town in Pierce County, Washington, USA. The town was founded in 1900 when the Northwest Improvement Company, a subsidiary of Northern Pacific Railway, started the Melmont coal mine; the town consisted of a schoolhouse, a train depot, a saloon, a hotel, rows of cottages that were used as housing for the miners. Each row accommodated a different nationality, the miners being self-segregated; the coal was used for use by Northern Pacific, when they switched from steam locomotives to diesel and electric models, the economic base of the town was destroyed. By 1902, the mine was producing coal to be sent 3 miles up the rails to Carbonado, where it was processed. During the sixteen years that the mine was worked, it produced 900,000 tons of coal, which accounted for 4% of the total output of Pierce County. On December 24, 1905, the house of Jack Wilson foreman of the mines, was bombed with a load of dynamite placed under the house; the explosion broke all the windows of the house, as well as those in the vicinity.

At the time and his daughter were sleeping in the house, but were unharmed by the explosion. David Steele, a miner at Melmont, was charged with the explosion, but was acquitted of the charges for lack of evidence. In 1915, the Melmont Post Office was closed, mail service to the town was done through Fairfax; the Northwest Improvement Company ceased operating in Melmont in 1918, but a few mines were opened by the Carbon Hill Coal Company, which operated from 1917 to 1919. At some point, the miners had affiliated themselves to the United Mine Workers as local #2963. By the early 1920s, the mines were all closed, a forest fire destroyed most of what was left of the town; the last resident of Melmont was Andrew Montleon, who lived in the remaining basement of the second schoolhouse. In 1920, the Melmont schoolhouse was torn down after Steven Poch bought it to use the lumber to build his own home. Today, all that remains of Melmont is part of the foundation of a bridge, a small building used for storing explosives, the foundation of the schoolhouse.

Daniels, Joseph. Mining History of Pierce County, Washington Coal Fields, 1860-1962, Washington Division of Geology and Earth Resources Open File Report OF 79-1. Hall, Nancy Irene. Carbon River Coal Country, Orting: Heritage Quest Press. Ramsey, Guy Reed. Postmarked Washington: Pierce County