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Topic: Real number line

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	Math 1010 on-line - The Real Number Line
		A positive number x corresponds to a point x units away from the origin to the right, and a negative number -x corresponds to a point on the line x units away from the origin to the left.
		We said that the number corresponds to a point on the real number line, but actually there is no useful distinction between a real number and its corresponding point on the real number line.
		Hence we may also say that a real number is on the real line, and a point on the real number line is a real number.
	www.math.utah.edu /online/1010/line (488 words)

	Encyclopedia :: encyclopedia : Real number (Site not responding. Last check: 2007-09-19)
		In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line.
		The real numbers are the central object of study in real analysis.
		The non-existence of a subset of the reals with cardinality strictly between that of the integers and the reals is known as the continuum hypothesis.
	www.hallencyclopedia.com /Real_number (1976 words)

	Real number
		In mathematics, the real numbers are intuitively defined as number s that are in one-to-one correspondence with the points on an infinite line —the number line.
		The nonexistence of a subset of the reals with cardinality strictly in between that of the integers and the reals is known as the continuum hypothesis.
		The reals carry a canonical measure, the Lebesgue measure, which is the Haar measure on their structure as a topological group normalised such that the unit interval [0,1] has measure 1.
	www.nebulasearch.com /encyclopedia/article/Real_number.html (1975 words)

	Learn more about Real number in the online encyclopedia. (Site not responding. Last check: 2007-09-19)
		Negative numbers began to be generally accepted in the 1600s and were invented by Muslim mathematicians.
		Occasionally, formal elements +∞ and -∞ are added to the reals to form the extended real number line, a compact space which is not a field anymore but retains many of the properties of the real numbers.
		Self-adjoint operatorss on a Hilbert space (for example, self-adjoint square complex matrices) generalize the reals in many respects: they can be ordered (though not totally ordered), they are complete, all their eigenvalues are real and they form a real associative algebra.
	www.onlineencyclopedia.org /r/re/real_number.html (2010 words)

	real number
		Real numbers stand in one-to-one correspondence with the points on a continuous line, known as the real number line, that stretches from zero to infinity in both directions.
		The name "real number" is a retronym, coined by René Descartes in response to the concept of imaginary numbers.
		Number systems that are even more general that the real numbers include the complex numbers and, of much more recent discovery, hyperreal numbers and surreal numbers.
	www.daviddarling.info /encyclopedia/R/real_number.html (176 words)

	transcendental number - a real number which is not the root of a polynomial equation with integer coefficients
		The set of real numbers can be divided into two subsets, the algebraic numbers and the transcendental numbers.
		Algebraic numbers are the roots of polynomial equations with integer coefficients.
		According to set theory, the number of algebraic numbers is countably infinite (i.e., they can be put in a one-to-one correspondence with the integers) while the number of transendental numbers is uncountably infinite.
	tonalsoft.com /enc/t/transcendental-number.aspx (402 words)

	Inequalities. Set Notation etc.
		If we draw a line, designate a point on the line to be zero, and choose a scale, then every point on the line corresponds uniquely to a real number, and vice versa:
		A bigger number will always be found to the right of a smaller number.
		The number -2 is excluded from the set, so you see an "empty bubble"; the number 5 is included in the set, so the bubble at 5 is "filled in."
	www.sosmath.com /algebra/inequalities/ineq02/ineq02.html (657 words)

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