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Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid in his work Elements . There are several proofs of the theorem.
In the 18th century there was widespread use of infinitesimals in calculus, though these were not really well defined. Calculus was put on firm foundations in the 19th century, and Robinson put infinitesimals in a rigorous basis with the introduction of nonstandard analysis in the 20th century. Fundamental theorem of algebra (see History).
The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry)
During Middle Ages, Euclid's Elements stood as a perfectly solid foundation for mathematics, and philosophy of mathematics concentrated on the ontological status of mathematical concepts; the question was whether they exist independently of perception or within the mind only (conceptualism); or even whether they are simply names of collection ...
In mathematics, Euclid numbers are integers of the form E n = p n # + 1, where p n # is the nth primorial, i.e. the product of the first n prime numbers. They are named after the ancient Greek mathematician Euclid , in connection with Euclid's theorem that there are infinitely many prime numbers.
Euclid (/ ˈ j uː k l ɪ d /; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. [2] Considered the "father of geometry", [3] he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century.
Any theorem in Euclidean geometry; Any theorem in Euclid's Elements, and in particular: Euclid's theorem that there are infinitely many prime numbers; Euclid's lemma, also called Euclid's first theorem, on the prime factors of products; The Euclid–Euler theorem characterizing the even perfect numbers; Geometric mean theorem about right ...