List of real analysis topics

This is a list of articles that are considered real analysis topics. Limit of a sequence Subsequential limit – the limit of some subsequence Limit of a function (see List of limits for a list of limits of common functions) One-sided limit – either of the two limits of functions of real variables x, as x approaches a point from above or below Squeeze theorem – confirms the limit of a function via comparison with two other functions Big O notation – used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions (see also list of mathematical series) Arithmetic progression – a sequence of numbers such that the difference between the consecutive terms is constant Generalized arithmetic progression – a sequence of numbers such that the difference between consecutive terms can be one of several possible constants Geometric progression – a sequence of numbers such that each consecutive term is found by multiplying the previous one by a fixed non-zero number Harmonic progression – a sequence formed by taking the reciprocals of the terms of an arithmetic progression Finite sequence – see sequence Infinite sequence – see sequence Divergent sequence – see limit of a sequence or divergent series Convergent sequence – see limit of a sequence or convergent series Cauchy sequence – a sequence whose elements become arbitrarily close to each other as the sequence progresses Convergent series – a series whose sequence of partial sums converges Divergent series – a series whose sequence of partial sums diverges Power series – a series of the form Taylor series – a series of the form Maclaurin series – see Taylor series Binomial series – the Maclaurin series of the function f given by f(x) = (1 + x) α Telescoping series Alternating series Geometric series Divergent geometric series Harmonic series Fourier series Lambert series Cesàro summation Euler summation Lambert summation Borel summation Summation by parts – transforms the summation of products of into other summations Cesàro mean Abel's summation formula Convolution Cauchy product –is the discrete convolution of two sequences Farey sequence – the sequence of completely reduced fractions between 0 and 1 Oscillation – is the behaviour of a sequence of real numbers or a real-valued function, which does not converge, but also does not diverge to +∞ or −∞; and is also a quantitative measure for that.

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En mathématiques, un nombre réel est un nombre qui peut être représenté par une partie entière et une liste finie ou infinie de décimales. Cette définition s'applique donc aux nombres rationnels, dont les décimales se répètent de façon périodique à partir d'un certain rang, mais aussi à d'autres nombres dits irrationnels, tels que la racine carrée de 2, π et e.

List of real analysis topics

This is a list of articles that are considered real analysis topics.

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