Extended real number line and Limit of a function

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Difference between Extended real number line and Limit of a function

Extended real number line vs. Limit of a function

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). 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.

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.

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Calculus

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.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Hausdorff space

In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.

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Indeterminate form

In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metrization theorem

In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.

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Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

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Projectively extended real 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.

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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.

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