Hi
Would some one explain to a complete newbie how/why the set of even integers less than 100 IS NOT well ordered?
Thanks
Pravin
Any non-empty subset of which is bounded below contains a smallest term. If that is what you mean by well ordering then yes to your question.
One again as I said the first time, theoretically any set can be well ordered, we just don't know what the order would be.
But I think you mean the usual order . Saying that any non-empty set contains a first term.
In order to be well-ordered, it's not enough for the whole set to have the least element: every nonempty subset must have its own least element. I can create a nonstandard order on Z by taking the standard order and declaring 0 less than any other element of Z. With this order, Z has the least element, but it's still not a well-ordering.
Every nonempty subset of Z with the standard order that is bounded from below is well-ordered.
Thanks. Let me write what I have understood from your reply.
1. Set of Positive integers from 5 to 75 is well ordered.
2. Set of Integers from -25 to 75 is well ordered? Yes or No
Please respond as this will confirm that I have understood it correctly.
Thanks once again
Pravin