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They may hear said 'irrational number' and some even remember the phrase, but very few really understand what it means. Well, irrational numbers are harder to understand than rational numbers, but I consider it worth the time and effort because they have some fascinating properties.
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www.homeschoolmath.net/teaching/irrational_numbers.php
www.homeschoolmath.net/teaching/irrational_numbers.php
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Irrational number - Wikipedia, the free encyclopedia
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In mathematics, an irrational number is any real number that is not a rational number—that is, it is a number which cannot be expressed as a fraction m / n , where m and n are integers, with...
en.wikipedia.org/wiki/Irrational_number
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What's a number? To paraphrase Albert Einstein, a number by itself has no significance and only deserves the designation of _number_ by virtue of its being a member of a group of objects with some shared characteristics. ... Will Rose suggested a different way of growing bn into an irrational number. Pick any number r known...
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www.cut-the-knot.org/do_you_know/numbers.shtml
www.cut-the-knot.org/do_you_know/numbers.shtml
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The latter proof makes it entirely obvious that unless a square root of an integer is an integer itself, it is bound to be irrational. Furthermore, the same argument applies to roots other than square. Unless it's an integer itself, a fifth root of an integer is an irrational number! ... The proofs above,
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www.cut-the-knot.org/proofs/sq_root.shtml
www.cut-the-knot.org/proofs/sq_root.shtml
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An irrational number is a real number which cannot be represented as a ratio of two integers. That is, if $x$ is irrational, then ... It $a$ is a real number and $a^n$ is irrational for some $n=2,3,\ldots$ then $a$ is irrational (proof).
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planetmath.org/encyclopedia/IrrationalNumber.html
planetmath.org/encyclopedia/IrrationalNumber.html
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It is not only irrational, that is, it cannot be expressed as the ratio of two integers, say p/q. It is transcendental, which means that it is ... This condition is more restrictive than saying a number is irrational. For example, the polynomial of degree '2', X^2 - 3=0, has the solution X = sqrt(3), which is irrational.
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www.newton.dep.anl.gov/askasci/math99/math99119.htm
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Irrational number summary with 16 pages of encyclopedia entries, essays, summaries, research information, and more. ... The set of irrational numbers is the set of real numbers that cannot be expressed as the ratio, or quotient, of two integers. Thus, an irrational number cannot be written in the form , where a and b...
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www.bookrags.com/Irrational_number
www.bookrags.com/Irrational_number
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Hutchinson encyclopedia article about irrational number. irrational number. Information about irrational number in the Hutchinson encyclopedia. irrational numbers ... and e (the base of natural logarithms, approximately 2.71828). If an irrational number is expressed as a decimal it would go on for ever without repeating.
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encyclopedia.farlex.com/irrational+number
encyclopedia.farlex.com/irrational+number
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It is part of the demonstration formulated by the Pythagoreans that the square root of 2 is an irrational number. The argument goes like this: If the 2 is rational, then it can be expressed as the ratio of integers p/q (since that is what "rational" means for numbers).
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www.friesian.com/pythag.htm
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