23 relations: Analytic function, Augustin-Louis Cauchy, Calculus, Cardinal number, Continuous function, Derivative, Divergent series, Division by zero, Extended real number line, François-Napoléon-Marie Moigno, Function (mathematics), Infinitesimal, L'Hôpital's rule, Limit (mathematics), Limit of a function, Limit point, Mathematical analysis, Natural logarithm, Point at infinity, Projectively extended real line, Real number, Undefined (mathematics), Zero to the power of zero.
In mathematics, an analytic function is a function that is locally given by a convergent power series.
Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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.
In mathematics, division by zero is division where the divisor (denominator) is zero.
In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).
Abbé François-Napoléon-Marie Moigno (15 April 1804 – 14 July 1884) was a French Catholic priest and one time Jesuit, as well as a physicist and author.
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
In mathematics, infinitesimals are things so small that there is no way to measure them.
In mathematics, and more specifically in calculus, L'Hôpital's rule or L'Hospital's rule uses derivatives to help evaluate limits involving indeterminate forms.
In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.
In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the number line by a point denoted.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In mathematics, undefined has several different meanings, depending on the context.
Zero to the power of zero, denoted by 00, is a mathematical expression with no obvious value.
0 divided by 0, 0 × ∞, 0/0, 0×∞, 0÷0, 1^∞, Equivalent infinitesimal, Equivalent infinitesimals, Indeterminate expression, Indeterminate expressions, Indeterminate forms, Indeterminate number, ∞ - ∞, ∞/∞, ∞0, ∞^0, ∞−∞.