Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx>
- Date: Wed, 30 Jan 2008 10:01:29 +0100
MoeBlee wrote:
On Jan 29, 7:28 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
Aatu Koskensilta wrote:
On 2008-01-29, in sci.math, Han de Bruijn wrote:
Whew! Now, _that_'s an explanation! What's the *!#!@$ difference !?
The locution "set closed under the successor function" has a perfectly
clear meaning while "applying the successor function an infinite
number of times" is meaningless.
Typical .. I'd rather say that they're exactly the same. Meaning: if you
accept the first then I see no reason why not accept the second. Talking
about "clear" ..
Because you're utterly ignorant of the formal language of set theory.
It is not apparent how, in the particular context, one would put
"apply the operaton and infinite number of times" into the language of
set theory, while it is quite clear how to put "closed under
successor" into the language of set theory. That YOU are ignorant of
how the language of set theory works doesn't entail that such
differences are not vitally important.
Any thing is only _perfectly clear_ if you can teach it to a machine.
Your "closed under successor" is not in that category. Neither is my
"apply the operation and infinite number of times", admittedly. But I
can't imagine any reason why yes accept the former and no the latter.
Han de Bruijn
.
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