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Mathematical fallacy. In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known ...
The day-year principle was partially employed by Jews [7] as seen in Daniel 9:24–27, Ezekiel 4:4-7 [8] and in the early church. [9] It was first used in Christian exposition in 380 AD by Ticonius, who interpreted the three and a half days of Revelation 11:9 as three and a half years, writing 'three days and a half; that is, three years and six months' ('dies tres et dimidium; id est annos ...
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
In mathematics, Euler's identity[ note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .
Fermat–Catalan conjecture. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many ...
G. H. Hardy, A Mathematician's Apology (1940) He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one. John Edensor Littlewood, Littlewood's Miscellany (1986) The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by ...
Ordinal analysis. In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories have the same proof-theoretic ordinal they are often equiconsistent, and if one theory has a larger proof-theoretic ordinal than another it can often prove the consistency of ...
Monty Hall problem. In search of a new car, the player chooses a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let ...