#
The Least Upper Bound Property
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LUB1:
Arbitrarily Large Integers

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LUB2:
Arbitrarily Small Positive Rational Numbers

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LUB3:
Integers Immediately Surrounding Any Real Number

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LUB4:
Fractions Immediately Surrounding Any Real Number

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LUB5:
Arbitrarily Close Approximation to Real Numbers by Rational Numbers

Converted [ in part ] by *Mathematica*
December 4, 2007;

Edited 12 May 2010