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As students progress, more kinds of numbers can be placed on the line, including fractions, decimal fractions, square roots, and transcendental numbers such as the circle constant π: Every point of the number line corresponds to a unique real number, and every real number to a unique point. [1]
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
Stern–Brocot tree. In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree . The Stern–Brocot tree was introduced independently by Moritz Stern ( 1858) and Achille ...
The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...
The list can go on to include the fractions 1 / 109 , 1 / 113 , 1 / 131 , 1 / 149 , 1 / 167 , 1 / 179 , 1 / 181 , 1 / 193 , 1 / 223 , 1 / 229 , etc. (sequence A001913 in the OEIS). Every proper multiple of a cyclic number (that is, a multiple having the same number of digits ...
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of rationals [3 ...
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