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Proof that only uses basic techniques
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
Elementary_proof
Proofs of the mathematical result that the rational number 22/7 is greater than π (pi) date back to antiquity. One of these proofs, more recently developed
Proof_that_22/7_exceeds_π
Reasoning for mathematical statements
proof is known since Euclid), but not that 2 2 {\displaystyle {\sqrt {2}}^{\sqrt {2}}} is irrational (this is true, but the proof is not elementary)
Mathematical_proof
Theorem in vector calculus
a uniform scalar field, the standard Stokes' theorem is recovered. The proof of the theorem consists of 4 steps. We assume Green's theorem, so what is
Stokes'_theorem
Characterization of how many integers are prime
proof development in Isabelle/HOL, Archive of Formal Proofs) The Prime Number Theorem: the "elementary" proof − An exposition of the elementary proof
Prime_number_theorem
Alternative decimal expansion of 1
without proof to infinite decimals. An elementary but rigorous proof is given below that involves only elementary arithmetic and the Archimedean property:
0.999...
Branch of pure mathematics
integers. Elementary number theory studies aspects of integers that can be investigated using elementary methods such as elementary proofs. Analytic number
Number_theory
Averages of repeated trials converge to the expected value
doi:10.2307/2323947. JSTOR 2323947. Another proof was given by Etemadi, Nasrollah (1981). "An elementary proof of the strong law of large numbers". Zeitschrift
Law_of_large_numbers
Obligation on a party in a dispute to provide sufficient warrant for their position
The burden of proof (Latin: onus probandi, shortened from Onus probandi incumbit ei qui dicit, non ei qui negat – the burden of proof lies with the one
Burden_of_proof_(philosophy)
Relationship between the rational roots of a polynomial and its extreme coefficients
Zero Theorem". MathWorld. Rational root theorem at PlanetMath. Another proof that nth roots of integers are irrational, except for perfect nth powers
Rational_root_theorem
Quickly converging computation of π
(476): 231–242, doi:10.2307/3619132, JSTOR 3619132, S2CID 125865215 Milla, Lorenz (2019), Easy Proof of Three Recursive π-Algorithms, arXiv:1907.04110
Gauss–Legendre_algorithm
On closed convex subsets in Hilbert space
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 −
Hilbert_projection_theorem
Solved prime-number problem
by Chebyshev, and a shorter but also advanced proof was given by Ramanujan. The following elementary proof was published by Paul Erdős in 1932, as one of
Proof_of_Bertrand's_postulate
Exponentially decreasing bounds on tail distributions of random variables
proof for the symmetric case, we simply define the random variable Yi = 1 − Xi, apply the same proof, and plug it into our bound. The following proof
Chernoff_bound
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
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Topics referred to by the same term
Elementary definition, in mathematical logic elementary OS, a Linux distribution Elementary particle, in particle physics Elementary proof Elementary
Elementary
Courcier. pp. 340–341. MacDivitt, A. R. G.; Yanagisawa, Yukio (1987). "An elementary proof that e is irrational". The Mathematical Gazette. 71 (457). London:
Proof_that_e_is_irrational
Approximate identity involving logarithms of primes
Selberg. The identity forms the crucial starting point in the first elementary proof for the prime number theorem, arrived at jointly by Selberg and Paul
Selberg's_identity
Mathematics award
Yuri I. Manin, with the first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized
Fields_Medal
Norwegian mathematician (1917–2007)
established this result by elementary means in March 1948, and by July of that year, Selberg and Paul Erdős each obtained elementary proofs of the prime number
Atle_Selberg
Theorem in topology
New elementary proofs of the Jordan curve theorem, as well as simplifications of the earlier proofs, continue to be carried out. Elementary proofs were
Jordan_curve_theorem
Theorem on prime numbers
crediting his student John Wilson for the discovery. Lagrange gave the first proof in 1771. There is evidence that Leibniz was also aware of the result a century
Wilson's_theorem
Type of polynomial used in Numerical Analysis
Polynomials in this form were first used by Bernstein in a constructive proof of the Weierstrass approximation theorem. With the advent of computer graphics
Bernstein_polynomial
Mathematical expression for linear operators
Jordan–Chevalley decomposition of x {\displaystyle x} . Q.E.D. This proof, besides being completely elementary, has the advantage that it is algorithmic: By the Cayley–Hamilton
Jordan–Chevalley decomposition
Jordan–Chevalley_decomposition
Theorem in functional analysis
topological vector spaces must be finite-dimensional. The following elementary proof does not utilize duality theory and requires only basic concepts from
Banach–Alaoglu_theorem
Gives conditions that guarantee the max–min inequality holds with equality
_{x\in X}\min _{y\in Y}f(x,y)=\min _{y\in Y}\sup _{x\in X}f(x,y).} An elementary proof of this theorem is given by Komiya. The following example shows that
Minimax_theorem
Number of partitions of an integer
Hardy–Ramanujan asymptotic approximation. Paul Erdős (1942) published an elementary proof of the asymptotic formula for p ( n ) {\displaystyle p(n)} . Techniques
Partition function (number theory)
Partition_function_(number_theory)
Mathematical analysis theorem
theorem applied to the sequence space ℓ 1 {\displaystyle \ell ^{1}} . An elementary proof can also be given. Tannery's theorem can be used to prove that the
Tannery's_theorem
System of arithmetic in proof theory
In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic
Elementary function arithmetic
Elementary_function_arithmetic
Theorem on the number of primes in arithmetic sequences
beginning of rigorous analytic number theory. Atle Selberg gave an elementary proof of this theorem in 1949. Dirichlet's theorem is proved by showing that
Dirichlet's theorem on arithmetic progressions
Dirichlet's_theorem_on_arithmetic_progressions
Theorem on edge-disjoint spanning trees
Tutte and Nash-Williams, both in 1961. In 2012, Kaiser gave a short elementary proof. For this article, we say that such a graph has arboricity t or is
Nash-Williams_theorem
Shape with three sides
ISBN 978-3-642-14441-7. Hungerbühler, Norbert (1994). "A short elementary proof of the Mohr-Mascheroni theorem". American Mathematical Monthly. 101
Triangle
Proofs in enumerative combinatorics
between them. The term "combinatorial proof" may also be used more broadly to refer to any kind of elementary proof in combinatorics. However, as Glass
Combinatorial_proof
Hungarian mathematician (1913–1996)
found a proof for Bertrand's postulate which proved to be far neater than Chebyshev's original one. He also discovered the first elementary proof for the
Paul_Erdős
Sum of inverse squares of natural numbers
an Elementary Exposition". Later, in 1982, it appeared in the journal Eureka, attributed to John Scholes, but Scholes claims he learned the proof from
Basel_problem
Mathematical proof at least partially generated by computer
computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations
Computer-assisted_proof
Every finite abelian extension of Q is contained within some cyclotomic field
Pratishthana, Pune, pp. 135–146, MR 1802379 Greenberg, M. J. (1974). "An Elementary Proof of the Kronecker-Weber Theorem". American Mathematical Monthly. 81
Kronecker–Weber_theorem
Characterization by prime factors of sums of two squares
elliptic functions. An elementary proof is based on the unique factorization of the Gaussian integers. Hirschhorn gives a short proof derived from the Jacobi
Sum_of_two_squares_theorem
Mathematical inequality about the convolution of two functions
enlarge the L 2 {\displaystyle L^{2}} norm). Young's inequality has an elementary proof with the non-optimal constant 1. We assume that the functions f , g
Young's convolution inequality
Young's_convolution_inequality
Math book by G. H. Hardy and E. M. Wright
Wright and was first published in 1938. The third edition added an elementary proof of the prime number theorem, and the sixth edition added a chapter
An Introduction to the Theory of Numbers
An_Introduction_to_the_Theory_of_Numbers
American computer programmer
Hao, Steven; He, Andrew; Li, Ray; Wu, Scott (September 4, 2014). "An Elementary Proof of the Cayley Formula Using Random Maps". arXiv:1409.1614 [math.CO]
Andrew_He
Theorem in topology
proof is that it uses only elementary techniques; more general results like the Borsuk-Ulam theorem require tools from algebraic topology. The proof uses
Brouwer_fixed-point_theorem
Mathematical problem of square numbers which are also square-pyramidal
until 1918 that G. N. Watson found a proof for this fact, using elliptic functions. More recently, elementary proofs have been published. The solution N
Cannonball_problem
Theorem in mathematical finite group theory
contained in a nilpotent subgroup. Alperin & Lyons (1971) gave a short elementary proof. Alperin, J. L.; Lyons, Richard (1971), "On conjugacy classes of p-elements"
Baer–Suzuki_theorem
The only quadratic pairing functions are the Cantor polynomials
number a {\displaystyle a} . In 2002, M. A. Vsemirnov published an elementary proof of this result. The theorem states that the Cantor polynomial is the
Fueter–Pólya_theorem
Monotone maps have countable discontinuities
that the result was previously well-known and had provided his own elementary proof for the sake of convenience. Prior work on discontinuities had already
Discontinuities of monotone functions
Discontinuities_of_monotone_functions
3 intersections of any triangle's adjacent angle trisectors form an equilateral triangle
algebraic proof by Alain Connes (1998, 2004) extending the theorem to general fields other than characteristic three, and John Conway's elementary geometry
Morley's_trisector_theorem
Branch of mathematical logic
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,
Proof_theory
Mathematical concept
Proof: Young's inequality with exponent 2 {\displaystyle 2} is the special case p = q = 2. {\displaystyle p=q=2.} However, it has a more elementary proof
Young's inequality for products
Young's_inequality_for_products
Expresses a Gauss sum using a product of values of the p-adic gamma function
gave another proof of the Gross–Koblitz formula ("Boyarsky" being a pseudonym of Bernard Dwork), and Robert (2001) gave an elementary proof. The Gross–Koblitz
Gross–Koblitz_formula
Mathematical proofs of basic properties of addition of the natural numbers
mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are used
Proofs involving the addition of natural numbers
Proofs_involving_the_addition_of_natural_numbers
Formula for area of a grid polygon
2307/2323172. JSTOR 2323172. MR 0812105. Trainin, J. (November 2007). "An elementary proof of Pick's theorem". The Mathematical Gazette. 91 (522): 536–540. doi:10
Pick's_theorem
Proposition in mathematics that is unproven
conjecture is a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture
Conjecture
Sum of the inverses of the positive integers cubed is irrational
11 (3): 268–272. doi:10.1112/blms/11.3.268. Zudilin, W. (2002). "An Elementary Proof of Apéry's Theorem". arXiv:math/0202159. Ю. В. Нестеренко (1996). Некоторые
Apéry's_theorem
Partial results found before the complete proof
a proof of the case in which n = 3. Euler had a complete and pure elementary proof in 1760, but the result was not published. Later, Euler's proof for
Proof of Fermat's Last Theorem for specific exponents
Proof_of_Fermat's_Last_Theorem_for_specific_exponents
Combinatorial identity
his collected works. A Czech mathematician Josef Kaucky published an elementary proof of the identity along with a history of the identity in 1964. Kaucky
Li_Shanlan_identity
Mathematical theorem
elementary proof can be reinterpreted using difference operators. Conversely, instead of using the generalized mean value theorem in the second proof
Symmetry of second derivatives
Symmetry_of_second_derivatives
Concept in Hlibert spaces mathematics
original proof of this theorem is due to K. Löwner who gave a necessary and sufficient condition for f to be operator monotone. An elementary proof of the
Trace_inequality
Mathematical concept
functions in L1(T), the case not covered by the development above. F. Riesz's proof of convexity, originally established by Hardy, is established directly without
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
Theorem in transcendental number theory
is transcendental. In particular, e1 = e is transcendental. (A more elementary proof that e is transcendental is outlined in the article on transcendental
Lindemann–Weierstrass_theorem
(1997). "An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space". The Annals of Probability
Gaussian isoperimetric inequality
Gaussian_isoperimetric_inequality
Mathematical proof expressed visually
In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident
Proof_without_words
Mathematical result
MR 2453366, S2CID 15911073. Dasgupta, Sanjoy; Gupta, Anupam (2003), "An elementary proof of a theorem of Johnson and Lindenstrauss" (PDF), Random Structures
Johnson–Lindenstrauss_lemma
Form of mathematical proof
up to the next one (the step). — Concrete Mathematics, page 3 margins. A proof by induction consists of two cases. The first, the base case, proves the
Mathematical_induction
Equations of degree 5 or higher cannot be solved by radicals
ISBN 1-4020-2186-0, MR 2110624, Zbl 1065.12001 Goldmakher, Leo, Arnold's Elementary Proof of the Insolvability of the Quintic (PDF) Khovanskii, Askold (2014)
Abel–Ruffini_theorem
Area of mathematical logic
compactness theorem have alternative proofs using ultraproducts, and they can be used to construct saturated elementary extensions if they exist. A theory
Model_theory
Theorem in algebraic number theory relating p-adic L-functions and ideal class groups
These proofs were modeled upon Ken Ribet's proof of the converse to Herbrand's theorem (the Herbrand–Ribet theorem). Karl Rubin found a more elementary proof
Main conjecture of Iwasawa theory
Main_conjecture_of_Iwasawa_theory
Every rigid motion is a screw displacement
the rigid motion can be accomplished through a screw motion. Another elementary proof of Mozzi–Chasles' theorem was given by E. T. Whittaker in 1904. Suppose
Chasles'_theorem_(kinematics)
Theorem in the mathematical formulation of quantum mechanics
mechanics". Arkiv för Fysik. 23: 307–340. Faure, Claude-Alain (2002). "An Elementary Proof of the Fundamental Theorem of Projective Geometry". Geometriae Dedicata
Wigner's_theorem
French mathematician (1842–1891)
Math.ucr.edu. 1996-11-26. Retrieved 2012-01-04. Ma, D. G. (1985). "An Elementary Proof of the Solutions to the Diophantine Equation 6 y 2 = x ( x + 1 ) (
Édouard_Lucas
Non-contradiction of a theory
complete. A consistency proof is a mathematical proof that a particular theory is consistent. The early development of mathematical proof theory was driven
Consistency
Proof by Alan Turing
Turing's proof is a proof by Alan Turing submitted on 12 November 1936 and first published in 1937 with the title "On Computable Numbers, with an Application
Turing's_proof
Sheaf cohomology on the étale site
more elementary proof of the Weil conjectures in these two cases: in general one expects to find an elementary proof whenever there is an elementary description
Étale_cohomology
Equivalence of notions of density for sets of multiples of integers
it in 1936. Their original proof used the Hardy–Littlewood Tauberian theorem; later, they published another, elementary proof. Ahlswede, Rudolf; Khachatrian
Davenport–Erdős_theorem
British-Lebanese mathematician (1929–2019)
returned to it, reworking the proof several times to understand it better. With Bott he worked out an elementary proof, and gave another version of it
Michael_Atiyah
On zeros of derivatives of cubic polynomials
theorem for rational functions "Carlson's proof of Marden's theorem" (PDF). Kalman, Dan (2008a), "An Elementary Proof of Marden's Theorem", The American Mathematical
Marden's_theorem
)\leq {\frac {4}{9\lambda ^{2}}}.} For a relatively elementary proof see. The rough idea behind the proof is that there are two cases: one where the mode
Vysochanskij–Petunin inequality
Vysochanskij–Petunin_inequality
Establishment of a theorem using inference from the axioms
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language)
Formal_proof
Theorem in projective geometry
short elementary proof of Pascal's theorem in the case of a circle was found by van Yzeren (1993), based on the proof in (Guggenheimer 1967). This proof proves
Pascal's_theorem
Result on the class group of certain number fields, strengthening Ernst Kummer's theorem
an extension using methods in the theory of modular forms. A more elementary proof of Ribet's converse to Herbrand's theorem, a consequence of the theory
Herbrand–Ribet_theorem
In mathematics, a statement that has been proven
logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses the inference rules of a deductive
Theorem
Theorem in integral geometry
ISBN 0-521-59362-X. MR 1608265. An elementary and self-contained proof was given by Beifang Chen in Chen, B. (2004). "A simplified elementary proof of Hadwiger's volume
Hadwiger's_theorem
Non-orientable surface with one edge
Fried, Eliot (2015). "Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution
Möbius_strip
Study of objects of arithmetic interest over infinite towers of number fields
theorem (the so-called Herbrand–Ribet theorem). Karl Rubin found a more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's Euler systems, described
Iwasawa_theory
Geometrical concept relating area and volume
Method". Encyclopedia Britannica. Reed, N. (December 1986). "70.40 Elementary proof of the area under a cycloid". The Mathematical Gazette. 70 (454): 290–291
Cavalieri's_principle
Mathematical theory
{\displaystyle |Y|\setminus |X|} . Björner and Tancer presented an elementary combinatorial proof and summarized a few generalizations. For smooth manifolds,
Alexander_duality
Logical incompatibility between two or more propositions
Post, in his 1921 "Introduction to a General Theory of Elementary Propositions", extended his proof of the consistency of the propositional calculus (i.e
Contradiction
Inequality about exponentiations of ''1+x''
equivalently x t ≥ 1 − ( 1 − x ) t . {\displaystyle xt\geq 1-(1-x)^{t}.} An elementary proof for 0 ≤ r ≤ 1 {\displaystyle 0\leq r\leq 1} and x ≥ − 1 {\displaystyle
Bernoulli's_inequality
Theorem in geometric group theory
simple proof of the theorem was found by Bruce Kleiner. Later, Terence Tao and Yehuda Shalom modified Kleiner's proof to make an essentially elementary proof
Gromov's theorem on groups of polynomial growth
Gromov's_theorem_on_groups_of_polynomial_growth
Ferguson Made use of a desk calculator 620 1947 Ivan Niven Gave a very elementary proof that π is irrational January 1947 D. F. Ferguson Made use of a desk
Chronology of computation of pi
Chronology_of_computation_of_pi
Product of numbers from 1 to n
composite, proving the existence of arbitrarily large prime gaps. An elementary proof of Bertrand's postulate on the existence of a prime in any interval
Factorial
Theorem in economics
relation ⪰ {\displaystyle \succeq } is countable. Jaffray gives an elementary proof to the existence of a continuous utility function. Preferences are
Utility representation theorem
Utility_representation_theorem
French mathematician (1822–1901)
simplified Hermite's original proof. In 1947, Ivan Niven exploited a technique of Hermite to give an elementary proof that π {\displaystyle \pi } is
Charles_Hermite
Number divisible only by 1 and itself
primes have been posed. Often having an elementary formulation, many of these conjectures have withstood proof for decades: all four of Landau's problems
Prime_number
Nigerian politician and mathematician
Wiles and Richard Taylor in 1994. He also claimed to have found an elementary proof to Fermat’s Last Theorem. This work was carried out at his Nanna Institute
Chike_Obi
Mapping from p forms to p-1 forms
to Élie or Henri?, MathOverflow, 2010-09-21, retrieved 2018-06-25 Elementary Proof of the Cartan Magic Formula, Oleg Zubelevich Eric Lengyel (2024). Projective
Interior_product
American mathematician (1912–1975)
Mathematical Association of America for his paper A Motivated Account of an Elementary Proof of the Prime Number Theorem. In 1974 he published a paper proving that
Norman_Levinson
Book by Carl E. Linderholm
advanced mathematical methods to prove results normally shown using elementary proofs. Although the aim is largely satirical, it also shows the non-trivial
Mathematics_Made_Difficult
\mathrm {d} x.} Carleman's inequality follows from the case p = 0. An elementary proof is sketched below. From the inequality of arithmetic and geometric
Carleman's_inequality
Sum of the inverses of the positive cubes
1070/RM2001v056n04ABEH000427, S2CID 250734661. Zudilin, Wadim (2002), "An elementary proof of Apéry's theorem", arXiv:math/0202159{{cite arXiv}}: CS1 maint: overridden
Apéry's_constant
ELEMENTARY PROOF
ELEMENTARY PROOF
Boy/Male
Indian
Proof
Boy/Male
Arabic, Muslim
Evidence; Proof
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Muslim
Proof
Boy/Male
Muslim
Evidence. Proof.
Surname or Lastname
English
English : from Middle English, Old French palmer, paumer (from palme, paume ‘palm tree’, Latin palma), a nickname for someone who had been on a pilgrimage to the Holy Land. Such pilgrims generally brought back a palm branch as proof that they had actually made the journey, but there was a vigorous trade in false souvenirs, and the term also came to be applied to a cleric who sold indulgences.Swedish (Palmér) : ornamental name formed with palm ‘palm tree’ + the suffix -ér, from Latin -erius ‘descendant of’.Irish : when not truly of English origin (see 1 above), a surname adopted by bearers of Gaelic Ó Maolfhoghmhair (see Milford) perhaps because they were from an ecclesiastical family.German : topographic name for someone living among pussy willows (see Palm 2).German : from the personal name Palm (see Palm 3).
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Arabic, Muslim
Another Name for God; Evidence; Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Girl/Female
Muslim
Guide, Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Muslim
Argument, Reasoning, Proof
Boy/Male
Muslim
Proof
Boy/Male
Indian
Proof
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu, Traditional
Witness; Justice; Proof; Cute Princess; Loved by Everyone; Grace; Purity; Pluck; Witness Truth; Queen; Princess; Real; Truth
Girl/Female
Muslim
Proof
Girl/Female
Biblical
Flight, proof, temptation, delicate.
Girl/Female
Indian
Witness; Proof
Boy/Male
Indian
Argument, Reasoning, Proof
Boy/Male
Arabic
Evidence; Proof; Distinction Between Truth and Falsehood
ELEMENTARY PROOF
ELEMENTARY PROOF
Girl/Female
Indian, Kannada, Tamil
Moon Light
Girl/Female
Tamil
Yagapriya | யாகபà¯à®°à®¿à®¯à®¾
Name of a Raga
Boy/Male
Hindu
Female
Portuguese
Feminine form of Portuguese Glaucio, GLAUCIA means "bluish-gray." Compare with masculine Glaucia.
Biblical
the Lord's feast
Girl/Female
Hindu, Indian
Supreme God
Boy/Male
Muslim
Esteem. Credit.
Girl/Female
Hindu, Indian, Malayalam, Marathi, Tamil, Telugu
Goddess Lakshmi
Surname or Lastname
English (southern counties)
English (southern counties) : apparently a variant of Hapgood.
Girl/Female
French
Great happiness.
ELEMENTARY PROOF
ELEMENTARY PROOF
ELEMENTARY PROOF
ELEMENTARY PROOF
ELEMENTARY PROOF
a.
Pertaining to rudiments or first principles; rudimentary; elementary.
a.
Elementary.
n.
An elementary piece of the mechanism of a lock.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
a.
Pertaining to, or treating of, the elements, rudiments, or first principles of anything; initial; rudimental; introductory; as, an elementary treatise.
n.
The whole alimentary, or enteric, canal.
adv.
According to elements; literally; as, the words, "Take, eat; this is my body," elementally understood.
a.
Elementary.
a.
Having only one principle or constituent part; consisting of a single element; simple; uncompounded; as, an elementary substance.
n.
The doctrine of the elementary requisites of mere thought.
a.
Relating to hypostasis, or substance; hence, constitutive, or elementary.
a.
Regulative.
a.
Capable of being leased; held by tenants.
n.
Elementariness.
n.
The state of being elementary; original simplicity; uncompounded state.
a.
Combined with arsenic; -- said some elementary substances or radicals; as, arseniureted hydrogen.
a.
Pertaining to aliment or food, or to the function of nutrition; nutritious; alimental; as, alimentary substances.
n.
Unorganized material; elementary matter.
a.
Elementary; rudimental.
a.
Pertaining to one of the four elements, air, water, earth, fire.