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Now, z differs from every number in the list (in fact, it differs from the i -th number in the i -th digit), and so it cannot be in the list. The set of real numbers is larger than the set of rational numbers.
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www.math.utah.edu/~pa/math/sets/realproof.html
www.math.utah.edu/~pa/math/sets/realproof.html
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Without getting technical, real numbers are all numbers that can be written as a possibly never repeating decimal fraction. For example, all rational numbers are real. Their decimal representations do repeat. Decimal fractions whose representation do not repeat are irrational.
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www.math.utah.edu/~alfeld/math/numbers.html
www.math.utah.edu/~alfeld/math/numbers.html
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I've always understood the real numbers as having a relatively simple axiomatic definition (e.g. [0]). I'll admit I didn't properly understand this entry, but it didn't even seem to acknowledge the existance of this kind of definition. ... ; "real number" is owned by djao. [ full author list (2) ]
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planetmath.org/encyclopedia/MathbbR.html
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The below list presents entries on real numbers in an order suitable for studying the subject. ... ; Anyone with an account can edit this entry. Please help improve it!; "topic entry on real numbers" is owned by matte. [ full author list (4) ]
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planetmath.org/encyclopedia/TopicEntryOnRealNumbers.htm...
planetmath.org/encyclopedia/TopicEntryOnRealNumbers.html
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Were the real numbers consistent? Would an inconsistency appear one day and much of the mathematical building come tumbling down? ... List all computer programs -- in fact they will all occur in the number c above. Create a new real number t by Cantor's diagonal argument whose n-th digit is defined as follows.
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www-history.mcs.st-and.ac.uk/HistTopics/Real_numbers_3....
www-history.mcs.st-and.ac.uk/HistTopics/Real_numbers_3.html
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Home | Register | Report Page ... Science Forum Index » Logic Forum » THIS IS A LIST OF REAL NUMBERS ... Posted: Sun May 08, 2005 4:49 am...
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www.groupsrv.com/science/about96436.html
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Definitions: Real Numbers is a set of numbers that includes both rational and irrational numbers ... So the following are examples of real numbers:
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www.pindling.org/Math/Learning/Basic_Math/Rationals/rea...
www.pindling.org/Math/Learning/Basic_Math/Rationals/real_numbers.html
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Sorry to come in on this dicussion of real numbers, decimals etc. so late, and perhaps this has been said before: there is an interesting paper by; ... Advances in Mathematics, (1975) 16, 278-304 that seems, to me at least, to adress a lot of the concerns expressed on this list about their construction and arithmetic.
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sunsite.utk.edu/math_archives/.http/hypermail/mathedu/f...
sunsite.utk.edu/math_archives/.http/hypermail/mathedu/feb98/0064.html
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We can also write one that will list the digits of the decimal expansion of the square root of 2. Similarly, there are computer programs that will compute the square roots of integers, ones that will compute cube roots, etc. ... In fact, for the irrational numbers that you encounter in your day-to-day life,
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www.math.hmc.edu/funfacts/ffiles/30004.8.shtml
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