Re: Cantor Confusion


"Arturo Magidin" <magidin@xxxxxxxxxxxxxxxxx> wrote in message
news:efj3bk$120f$1@xxxxxxxxxxxxxxxxxxxxx
In article <N_YSg.1208$3E2.403@xxxxxxxxxxxxxxxxxxxxx>,
Poker Joker <Poker@xxxxxxxxx> wrote:

"Arturo Magidin" <magidin@xxxxxxxxxxxxxxxxx> wrote in message
news:efgfhd$261u$1@xxxxxxxxxxxxxxxxxxxxx
In article <1159410937.013643.192240@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<the_wign@xxxxxxxxx> wrote:
Cantor's proof is one of the most popular topics on this NG. It
seems that people are confused or uncomfortable with it, so
I've tried to summarize it to the simplest terms:

1. Assume there is a list containing all the reals.
2. Show that a real can be defined/constructed from that list.
3. Show why the real from step 2 is not on the list.
4. Conclude that the premise is wrong because of the contradiction.

This is hardly the simplest terms. Much simpler is to do a ->direct<-
proof instead of a proof by contradiction.

1. Take ANY list of real numbers.
2. Show that a real can be defined/constructed from that list.
3. Show that the real from step 2 is not on the list.
4. Conclude that no list can contain all reals.


How can it be simpler if the list can be ANY list instead of a
particular one.

Because a direct proof is simpler than a proof by contradiction.

ANY list opens up more possiblities than
a single list.

Any list does not require you to assume that there is a "single list"
which some some particular property.

======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

We all noticed you neglected this logic:

if its true for ANY list, then it must be
true for a specific list. So if considering a single specific list
shows a flaw, then looking at ANY (ALL of them) list doesn't
help.



.

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