...with any element $a$ also contains the sum $a+1$, is necessarily the whole of $\mathbf{N}$. See [[Natural sequence]]; [[Arithmetic, formal]].
...lign="top"> , ''The history of mathematics from Antiquity to the beginning of the XIX-th century'' , '''1''' , Moscow (1970) (In Russian)</TD></TR>
2 KB (319 words) - 19:08, 5 February 2016
...ich the counters (bones, pebbles, etc.) were moved. The Chinese equivalent of the abacus — swan-pan — was used in the Far East, while the "schetysch
...> <TD valign="top"> W.W. Rouse Ball, "A short account of the history of mathematics" , Dover, reprint (1960) pp. 123–125</TD></TR></table>
674 bytes (100 words) - 17:27, 7 February 2011
An algebraic equation of degree three, ''i.e.'' an equation of the form
beginning of that century, S. Ferro solved the equation $x^3+px=q$, where
2 KB (312 words) - 19:38, 15 March 2023
A nice illustration of some of the simpler properties of (countably) infinite sets.
There is also room for an infinity of new guests. Indeed, shift the existing guest in room $1$ to room $2$, the o
2 KB (243 words) - 21:41, 14 April 2014
...es of an equilateral triangle and each of the remaining numbers is the sum of the two numbers above it to the left and right:
there appear the coefficients of the expansion of the binomial $(a+b)^{n}$.
3 KB (379 words) - 07:44, 4 November 2023
...r the solution of the problem of the [[Quadrature of the circle|quadrature of the circle]]. For example: the [[Dinostratus quadratrix|dinostratus quadrat
...lign="top">[a1]</TD> <TD valign="top"> Th.L. Heath, "A history of Greek mathematics" , '''1–2''' , Dover, reprint (1981)</TD></TR>
1 KB (158 words) - 18:18, 19 October 2014
...ers|coprime]] $(k + 1)$-tuple together with $n$. This is a generalisation of Euler's [[totient function]], which is $J_1$.
...d) = n^k $. The [[Average order of an arithmetic function|average order]] of $J_k(n)$ is $c n^k$ for some $c$.
1 KB (172 words) - 13:07, 19 March 2023
...d, in general, two elements of a [[Euclidean ring]]) or the common measure of two intervals. It was described in geometrical form in Euclid's Elements (3
...tive integers $a \ge b$, the method is as follows. Division with remainder of $a$ by $b$ always leads to the result $a = n b + b_1$, where the quotient $
2 KB (351 words) - 20:40, 16 November 2023
...30 : ~/encyclopedia/old_files/data/N067/N.0607960 Numbers, representations of
...symbols began to appear, so number systems began to vary in the character of their numerical signs and in the principles governing the form in which the
8 KB (1,143 words) - 08:03, 6 June 2020
...s, recursive functions, normal algorithms, and others — one may, by virtue of Church' thesis, restrict oneself to intuitively obvious constructions, and
...cannot be solved in the framework of this or that precision of the notion of algorithm.
3 KB (422 words) - 18:10, 12 December 2014
...ion of numbers (cf. [[Numbers, representations of|Numbers, representations of]]).
...rom about 3000–2500 B.C.) there were individual signs to denote the powers of ten (up to $10^7$).
3 KB (570 words) - 20:06, 11 April 2014
...lem can be reduced to finding a function $y(x)$ that constitutes a minimum of the functional
where $a$ and $b$ are the abscissas of points $A$ and $B$. The brachistochrone is a [[Cycloid|cycloid]] with a hor
2 KB (275 words) - 19:39, 29 April 2014
...rrently charged for an individual insurance contract be a weighted average of the form
is the observed mean claim amount per unit of risk exposed for the individual and $ \mu $
5 KB (696 words) - 17:31, 5 June 2020
$#C+1 = 30 : ~/encyclopedia/old_files/data/E036/E.0306840 Exhaustion, method of
...ns of antiquity in order to determine areas and volumes. The name "method of exhaustion" was introduced in the 17th century.
3 KB (471 words) - 19:38, 5 June 2020
"a history of Hilbert’s program for the foundations of mathematics, initiated by his Problems Address given in Paris, 1900" -- see [[Hilbert p
...ed to” (proved indirectly as a result of proving directly) the consistency of analysis:<ref>Hilbert (1902) §2</ref>
15 KB (2,329 words) - 14:32, 19 March 2023
Out of 16 formulas, 16 were replaced by TEX code.-->
...er must provide a reserve, $V _ { t }$, which by statute is the mean value of future discounted benefits less premiums. Splitting into payments before an
5 KB (787 words) - 16:55, 1 July 2020
...od for obtaining the incomplete fraction and the remainder in the division of a polynomial
...coefficients $a,a_0,\ldots,a_n$ lie in a certain field, e.g. in the field of complex numbers. Any polynomial $f(x)$ can be uniquely represented in the f
3 KB (445 words) - 18:09, 1 October 2017
...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al
'''Summary.''' A physician and writer, the creator of John Bull,
10 KB (1,512 words) - 07:24, 25 March 2023
...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al
The second of three sons of François Reymond, Écuyer,
7 KB (1,099 words) - 19:39, 8 March 2024
...eory of functions of a real variable typically involves a wide application of set-theoretic methods, along, naturally, with classical methods.
...rnoulli, J. d'Alembert, J.L. Lagrange, and others), although the formation of this theory took place in the 19th century (J. Fourier, A.L. Cauchy, N.I. L
11 KB (1,738 words) - 18:15, 24 March 2018