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The order of the natural numbers shown on the number line. A number line is a graphical representation of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.
As noted above, the absolute value of a real or complex number is the distance from that number to the origin, along the real number line, for real numbers, or in the complex plane, for complex numbers, and more generally, the absolute value of the difference of two real or complex numbers is the distance between them.
In 1835 Giusto Bellavitis introduced the idea of equipollent directed line segments which resulted in the concept of a vector as an equivalence class of such segments.. The term vector was coined by W. R. Hamilton around 1843, as he revealed quaternions, a system which uses vectors and scalars to span a four-dimensional space.
For numbers, the absolute value of a number is commonly applied as the measure of units between a number and zero. In vector spaces, the Euclidean norm is a measure of magnitude used to define a distance between two points in space. In physics, magnitude can be defined as quantity or distance.
A comparison of the letter O and the number 0. Traditionally, many print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0. [1] Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0.
A point on number line corresponds to a real number and vice versa. [15] Usually, integers are evenly spaced on the line, with positive numbers are on the right, negative numbers on the left. As an extension to the concept, an imaginary line representing imaginary numbers can be drawn perpendicular to the number line at zero. [16]
It is believed that a notation to represent numbers was first developed at least 50,000 years ago. [3] Early mathematical ideas such as finger counting [4] have also been represented by collections of rocks, sticks, bone, clay, stone, wood carvings, and knotted ropes. The tally stick is a way of counting dating back to the Upper Paleolithic.
In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.