Function (mathematics) and Graph of a function

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Difference between Function (mathematics) and Graph of a function

Function (mathematics) vs. Graph of a function

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity. In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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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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Derivative

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).

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Foundations of mathematics

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.

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Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

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Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Science

R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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Vertical line test

In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not.

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