Ordered numbers - limited or not

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Thread starter highmath
Start date Oct 31, 2018
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highmath

Thread starter
Oct 31, 2018

How many ways we can order numbers?
Is there infinity ways to order numbers?
Is there a proof of it?

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Evgeny.Makarov

Gold Member

MHB

Nov 1, 2018

Well, two numbers, for example, can be ordered in two ways. If we allow partial orders, that is, allow elements $x$ and $y$ such that none of $x<y$, $y<x$ and $x=y$ holds, then there are three ways to order two numbers.

Ordered numbers - limited or not

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Ordered numbers - limited or not

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