🚀 go-pugleaf

On Mar 13, 12:07 pm, Jim Burns <burns...@osu.edu> wrote:
> On 3/12/2011 10:31 AM, Graham Cooper wrote:
> > SHOW ME A DIGIT ON THE DIAGONAL THAT
> > EQUALS D AND EQUALS D+1
> > ---------------------------------
> > THAT is your entire argument!
> > THAT is your proof of BIGGER THAN INFINITY!
> That obviously cannot be done. All of us
> "standard theoreticians" agree with you,
> although Transfer Principle refuses to jump
> one way or the other, as near as I can tell.

If _both_sides_ actually agree on something, then I _don't_
disagree with the _unanimous_ consensus. I only "refuse to
jump one way or the other" when there's at least one _actual_
poster on each side of the debate. I don't disagree with a
unanimous consensus because I'd have _no_one_ to defend.

> The rest of the argument shows why you have to
> be able to do this impossible thing in order to
> list all of the real numbers -- which is why
> it is "obvious" (after some thought) that
> THE REAL NUMBERS CANNOT BE LISTED.
> You apparently understand all this.
> Why then are you trying to disprove a proven
> thing?

... proven in ZFC, that is.

> You might as well add to 2 to 2 over and
> over again until you get something other than 4.

Every time someone mentions "2+2=4," someone else usually
mentions piano interval arithmetic, in which a major 2nd
plus a major 2nd is a major 3rd. For some reason, those on
the standard side are _more_ willing to accept a theory in
which 2+2 is something other than 4 (such as 3, for pianos)
than they would accept a theory where there are as many
reals as naturals.

> The ironic thing about all this is that
> EVEN IF YOU DID disprove Cantor (Let's say
> you do this in some unimaginably bizarre
> alternate universe)

... or an unimaginably "bizarre" _theory_, like NFU, or
zuhair's ND, and so on ...

> Why not give it a rest, and go do something
> where there is at least a chance of success,
> like teaching pigs to fly?

The existence of NFU and zuhair's ND show that disproving
Cantor _does_ have more a chance of success than making
pigs fly or spotting UFO's.