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The number 0 may or may not be considered a natural number, [70] [71] but it is an integer, and hence a rational number and a real number. [72] All rational numbers are algebraic numbers, including 0. When the real numbers are extended to form the complex numbers, 0 becomes the origin of the complex plane.
The origin of a Cartesian coordinate system. In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same ...
Thus the origin has coordinates (0, 0), and the points on the positive half-axes, one unit away from the origin, have coordinates (1, 0) and (0, 1). In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards.
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
In mathematics, the notion of number has been extended over the centuries to include zero (0), [3] negative numbers, [4] rational numbers such as one half (), real numbers such as the square root of 2 and π, [5] and complex numbers [6] which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or ...
It can be made to hold for all real numbers by extending the definition of negation to include zero and negative numbers. Specifically: The negation of 0 is 0, and; The negation of a negative number is the corresponding positive number. For example, the negation of −3 is +3. In general,
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.