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'well-ordering principle for natural numbers'
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| Title of object: |
well-ordering principle for natural numbers |
| Canonical Name: |
WellOrderingPrinciple |
| Type: |
Axiom |
| Created on: |
2001-10-16 08:37:55 |
| Modified on: |
2007-06-21 21:11:30 |
| Classification: |
msc:06F25 |
Preamble:
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Content:
\PMlinkescapeword{equivalent}
Every nonempty set $S$ of natural numbers contains a least element; that is, there is some number $a$ in $S$ such that $a \leq b$ for all $b$ belonging to $S$.\\
Beware that there is another statement (which is equivalent to the axiom of choice) called the ``well-ordering principle." It asserts that every set can be well-ordered.
Note that the well-ordering principle for natural numbers is equivalent to the principle of mathematical induction (or, the principle of finite induction). |
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