In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain theorems, like the prime number theorem, could only be proved by invoking "higher" mathematical theorems or techniques. However, as time progresses, many of these results have also been subsequently reproven using only elementary techniques.
While there is generally no consensus as to what counts as elementary, the term is nevertheless a common part of the mathematical jargon. An elementary proof is not necessarily simple, in the sense of being easy to understand or trivial. In fact, some elementary proofs can be quite complicated — and this is especially true when a statement of notable importance is involved.[1]
^Diamond, Harold G. (1982), "Elementary methods in the study of the distribution of prime numbers", Bulletin of the American Mathematical Society, 7 (3): 553–89, doi:10.1090/S0273-0979-1982-15057-1, MR 0670132.
an elementaryproof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that...
calculated. An elementaryproof is a proof which only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make...
proof development in Isabelle/HOL, Archive of Formal Proofs) The Prime Number Theorem: the "elementary" proof − An exposition of the elementaryproof...
"Rational Zero Theorem". MathWorld. RationalRootTheorem at PlanetMath Another proof that nth roots of integers are irrational, except for perfect nth powers...
between them. The term "combinatorial proof" may also be used more broadly to refer to any kind of elementaryproof in combinatorics. However, as Glass...
New elementaryproofs of the Jordan curve theorem, as well as simplifications of the earlier proofs, continue to be carried out. Elementaryproofs were...
Courcier. pp. 340–341. MacDivitt, A. R. G.; Yanagisawa, Yukio (1987). "An elementaryproof that e is irrational". The Mathematical Gazette. 71 (457). London:...
a proof is beautiful when such a proof finally gives away the secret of the theorem.... — Gian-Carlo Rota (1977, pp.173–174, pp.181–182) Elementary A...
electron Elementary definition, in mathematical logic elementary OS, a Linux distribution Elementary particle, in particle physics Elementaryproof Element...
analysis in 1896, but an elementaryproof was found only in 1949 by Erdős and Selberg. The term is somewhat ambiguous: for example, proofs based on complex Tauberian...
that x − m {\displaystyle x-m} is orthogonal to C . {\displaystyle C.} Proof that a minimum point y {\displaystyle y} exists Let δ := inf c ∈ C ‖ x −...
com. 19 June 2008. Retrieved 2012-06-09. Etemadi, N. Z. (1981). "An elementaryproof of the strong law of large numbers". Wahrscheinlichkeitstheorie Verw...
{K}{n}}\right)b_{K,n}(x)=B_{n}(f)(x)} The probabilistic proof can also be rephrased in an elementary way, using the underlying probabilistic ideas but proceeding...
established this result by elementary means in March 1948, and by July of that year, Selberg and Paul Erdős each obtained elementaryproofs of the prime number...
an Elementary Exposition". Later, in 1982, it appeared in the journal Eureka, attributed to John Scholes, but Scholes claims he learned the proof from...
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition...
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,...
Hao, Steven; He, Andrew; Li, Ray; Wu, Scott (September 4, 2014). "An ElementaryProof of the Cayley Formula Using Random Maps". arXiv:1409.1614. Wu, Scott;...
Global Information