On Thursday, February 20, 2014 1:39:24 PM UTC+2, muec...@rz.fh-augsburg.de wrote: > Zeitgeist on the odds of my students to understand transfinite set theory:" if they can be convinced that what their senses tell them may be Not be the whole picture, then they may have a chance."
What a dunce. Tsk, tsk. Not worthy of addressing seriously.
> Virgil, appearing as Wisely Non-Theist: "There are 'more' real numbers than there are finite definitions to define them with, so most reals can only be defined collectively, not individually."
Obvious rot, because the set of natural numbers consists of elements whose definitions are ALL finite.
> Ben Bacarrisse emphasized: "They are not 'entirely undefinable'. The set of them can be defined." And he added: "You can know things about the set. For example, that it can't be bijected with N."
A bumbling moron. Probably a close second or third to the forum idiot (Wizard of Oz). If the real numbers are not entirely definable, then one can't even begin to talk about a countable set, because wait for it, ... in order for a set to be countable, ALL of its elements must have names (read as: defined). The bijection part is possible only if one knows ALL the elements one is dealing with. And here is a paradox: Only a mainstream moron will attempt to list a set not knowing that all its elements don't have names.
> William P. Hughes: "A subcollection of a listable collection may not be listable."
I hear Star Trek music playing when I read that.
> Alan Smaill: "After all, since matheology accepts undefinable real numbers, then why are you trying to suggest that it does not accept undefinable enumerations?"
I don't know anything about matheology, so I'll withhold comment on that one.
> That is true. I never got a grasp of this idea: Why should undefinable definable enumerations (aka lists) be exempt from the list of unlisted exemptions?
If you use a term like "undefinable definable enumerations", then you are already in serious trouble with mathematics! Your logic is nonsense.