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Concept# Number line

Summary

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
The integers are often shown as specially-marked points evenly spaced on the line. Although the image only shows the integers from –3 to 3, the line includes all real numbers, continuing forever in each direction, and also numbers that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers.
In advanced mathematics, the number line can be called the real line or real number line, formally defined as the set R of all real numbers. It is viewed as a geometric space, namely the real coordinate space of dimension one, or the Euclidean space of dimension one – the Euclidean line. It can also be thought of as a vector space (or affine space), a metric space, a topological space, a measure space, or a linear continuum.
Just like the set of real numbers, the real line is usually denoted by the symbol R (or alternatively, , the letter “R” in blackboard bold). However, it is sometimes denoted R1 or E1 in order to emphasize its role as the first real space or first Euclidean space.
The first mention of the number line used for operation purposes is found in John Wallis's Treatise of algebra. In his treatise, Wallis describes addition and subtraction on a number line in terms of moving forward and backward, under the metaphor of a person walking.
An earlier depiction without mention to operations, though, is found in John Napier's A description of the admirable table of logarithmes, which shows values 1 through 12 lined up from left to right.
Contrary to popular belief, Rene Descartes's original La Géométrie does not feature a number line, defined as we use it today, though it does use a coordinate system. In particular, Descartes's work does not contain specific numbers mapped onto lines, only abstract quantities.

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