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> why real numbers are somehow unorderable They are orderable ... For all x, y in R, either x >= y or x < y. But R is not bounded (no inf, sup) and therefore
by nanis 5y ago
> why real numbers are somehow unorderable
They are orderable ... For all x, y in R, either x >= y or x < y.
But R is not bounded (no inf, sup) and therefore has no minimum and no maximum.
- threatofrain 5y agoWhat's the consequence of extending the reals with infinities, as my textbook for real analysis does?
- rocqua 5y agoThat every closed set has a maximum and a minimum. Relatedly, every set gets a supremum and an infumum. (The first two must be members of the set. The second two can lie outside the set). Without the extension, you need to make an exception for unbounded sets with the above rules.