3 ms·

What's the well ordered one about?

• newt0311 18y ago
  A well ordering is just some way of ordering a set made formal. Basically, if you have a set, you can find a relation such that any subset will have a least element. I should also point out that the example given of a set that is not well-ordered is wrong. The proof was found to be erroneous.
• andreyf 18y ago
  A better example is the well-ordering of the reals. From wikipedia: From the [axioms of math] one can show that there is a well-order of the reals; it is also possible to show that [those axioms] alone are not sufficient to prove the existence of a definable (by a formula) well-order of the reals. http://en.wikipedia.org/wiki/Well-order http://en.wikipedia.org/wiki/Well-order So you can prove that set of real numbers can be well-ordered, but you can also prove that an order cannot be defined. Kind of how God exists, but cannot be perceived or comprehended ;) (or maybe not)
  • Dilpil 18y ago
    Absolutely nothing like the proposition that god exists, and I wag my finger at you for associating the concrete facts of mathematics with superstitious claims backed up by hearsay.
    • ars 18y ago
      This is not reddit.