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# 1 + 2 + 3 + 4 + ⋯

The infinite series whose terms are the natural numbers is a divergent series. 

61 relations: A Disappearing Number, Additive identity, Alternating series, Analytic continuation, Asymptote, Bernoulli number, Bosonic string theory, Bounded function, Brady Haran, Cesàro summation, Complex analysis, David Leavitt, Dirichlet eta function, Dirichlet series, Divergent series, Edward Frenkel, Euler–Maclaurin formula, G. H. Hardy, Goddard–Thorn theorem, Grandi's series, Infinity, John C. Baez, John Edensor Littlewood, Limit of a sequence, Luboš Motl, Mollifier, Monstrous moonshine, Morris Kline, Natural number, One-sided limit, Power series, Pythagoreanism, Quantum field theory, Quantum harmonic oscillator, Ramanujan summation, Real analysis, Riemann zeta function, Scalar field, Scientific American, Sequence, Series (mathematics), Simon McBurney, Smithsonian (magazine), Smoothness, Srinivasa Ramanujan, String theory, Support (mathematics), Terence Tao, Term test, The Indian Clerk, ... Expand index (11 more) »

## A Disappearing Number

A Disappearing Number is a 2007 play co-written and devised by the Théâtre de Complicité company and directed and conceived by English playwright Simon McBurney.

In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.

## Alternating series

In mathematics, an alternating series is an infinite series of the form with an > 0 for all n.

## Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.

## Asymptote

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

## Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.

## Bosonic string theory

Bosonic string theory is the original version of string theory, developed in the late 1960s.

## Bounded function

In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.

Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.

## Cesàro summation

In mathematical analysis, Cesàro summation (also known as the Cesàro mean) assigns values to some infinite sums that are not convergent in the usual sense.

## Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

## David Leavitt

David Leavitt (born June 23, 1961) is an American novelist, short story writer, and biographer.

## Dirichlet eta function

In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0: This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, &zeta;(s) &mdash; and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted &zeta;*(s).

## Dirichlet series

In mathematics, a Dirichlet series is any series of the form where s is complex, and a_n is a complex sequence.

## Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

## Edward Frenkel

Edward Vladimirovich Frenkel (sometimes spelled Э́двард Фре́нкель; born May 2, 1968) is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics.

## Euler–Maclaurin formula

In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums.

## G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.

## Goddard–Thorn theorem

In mathematics, and in particular, in the mathematical background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem describing properties of a functor that quantizes bosonic strings.

## Grandi's series

In mathematics, the infinite series 1 - 1 + 1 - 1 + \dotsb, also written \sum_^ (-1)^n is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703.

## Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

## John C. Baez

John Carlos Baez (born June 12, 1961) is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California.

## John Edensor Littlewood

John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

## Luboš Motl

Luboš Motl (born December 5, 1973) is a Czech theoretical physicist.

## Mollifier

In mathematics, mollifiers (also known as approximations to the identity) are smooth functions with special properties, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution.

## Monstrous moonshine

In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the ''j'' function.

## Morris Kline

Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## One-sided limit

In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.

## Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

## Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

## Quantum field theory

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.

## Quantum harmonic oscillator

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator.

## Ramanujan summation

Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.

## Real analysis

In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.

## Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

## Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.

## Scientific American

Scientific American (informally abbreviated SciAm) is an American popular science magazine.

## Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

## Simon McBurney

Simon Montagu McBurney, OBE (born 25 August 1957) is an English actor, writer and director.

## Smithsonian (magazine)

Smithsonian is the official journal published by the Smithsonian Institution in Washington, D.C. The first issue was published in 1970.

## Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

## Srinivasa Ramanujan

Srinivasa Ramanujan (22 December 188726 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable.

## String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

## Support (mathematics)

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

## Terence Tao

Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics.

## Term test

In mathematics, the nth-term test for divergenceKaczor p.336 is a simple test for the divergence of an infinite series.

## The Indian Clerk

The Indian Clerk is a biographical novel by David Leavitt, published in 2007.

## The New York Times

The New York Times (sometimes abbreviated as The NYT or The Times) is an American newspaper based in New York City with worldwide influence and readership.

## Thomas John I'Anson Bromwich

Thomas John I'Anson Bromwich (1875–1929) was an English mathematician, and a Fellow of the Royal Society.

## Transverse wave

A transverse wave is a moving wave that consists of oscillations occurring perpendicular (right angled) to the direction of energy transfer (or the propagation of the wave).

## Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.

## University of Nottingham

The University of Nottingham is a public research university in Nottingham, United Kingdom.

## Zeta function regularization

In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.

## 1 + 1 + 1 + 1 + ⋯

In mathematics,, also written \sum_^ n^0, \sum_^ 1^n, or simply \sum_^ 1, is a divergent series, meaning that its sequence of partial sums does not converge to a limit in the real numbers.

## 1 + 2 + 4 + 8 + ⋯

In mathematics, is the infinite series whose terms are the successive powers of two.

## 1 − 2 + 3 − 4 + ⋯

In mathematics, 1 − 2 + 3 − 4 + ··· is the infinite series whose terms are the successive positive integers, given alternating signs.

## 13 Reasons Why

13 Reasons Why (stylized onscreen as TH1RTEEN R3ASONS WHY) is an American teen drama web television series developed for Netflix by Brian Yorkey, based on the 2007 novel Thirteen Reasons Why by Jay Asher.

## References

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