Only if you accept excluded middle.
That depends on what you mean by "well-ordered". My philosophy of doing constructive mathematics (mathematics without excluded middle, and often with other restrictions) is that one should define terms as much as possible so that the usual theorems (including the theorems that the motivating examples are examples) become true, so long as the definitions are classically (that is using the usually accepted axioms) equivalent to the usual definitions.
As the motivating example of a well-ordered set is the set of natural numbers, we should use a defi...
Update: Discussion has moved on to a new thread.
The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: