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## Main Question or Discussion Point

Hi

Does anybody know if the irrational numbers have the least upper bound property?

Does anybody know if the irrational numbers have the least upper bound property?

- Thread starter RediJedeye
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- #1

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Hi

Does anybody know if the irrational numbers have the least upper bound property?

Does anybody know if the irrational numbers have the least upper bound property?

- #2

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The set of irrationals less than zero is nonempty (it contains -pi, for example) and is bounded above (by pi, for example) yet has no least upper bound. So the irrationals do not satisfy the LUB property.Hi

Does anybody know if the irrational numbers have the least upper bound property?

Of course zero is a LUB for that set

- #3

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Cool that makes perfect sense thanks for the help.

- #4

Bacle2

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consider the intervals (-oo,q) . Notice that the LUB of a subset of real numbers is

a limit point of that set S . So if a subset S of R does not contain all its limit points you

can constructuct a subset of S that does not contain its LUB-- so that closed subsets

contain their LUB's. Think of the relation with completeness of a set...

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