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where ≤ be the usual ordering.
Let and be usual ordering.
Let endowed with usual ordering.
Example 2.1 Let X = R with a usual ordering.
Let X = [0, 1] be endowed with usual ordering.
[1] Let (mathcal X = [0, 1]) be endowed with the usual ordering.
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Any of the usual ordered pair constructions works in NFU.
(The real numbers are not well-ordered in their usual order: just consider an open interval. Meanwhile, N is the simplest infinite well-ordered set).
In fact, though, it is the usual order of things.
Not the usual order of things, but not impossible.
For the usual order has been turned on its head.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com