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Food for thought, camera access to events



 
 
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  #31  
Old April 7th 13, 09:45 PM posted to rec.photo.digital.slr-systems
Robert Coe
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Posts: 4,901
Default Food for thought, camera access to events

On Sun, 7 Apr 2013 09:17:55 -0700 (PDT), Rob Ranger
wrote:
: On Apr 6, 11:35*am, Robert Coe wrote:
: On Fri, 5 Apr 2013 22:17:01 +0200, Wolfgang wrote:
:
: : Robert Coe wrote:
: : On Tue, 2 Apr 2013 18:37:25 +0200, Wolfgang Weisselberg
: :
: : : I shouldn't bother, but I'm going to call your bluff. Please tell us what the
: : : first two infinite numbers are
: :
: : [...]
: :
: : No, they are not sets. They are the (infinite) numbers of *members*
: : incorporated in two different sets. I leapt to the conclusion that transfinite
: : arithmetic is beyond your reach, and you seem to have proven me correct.
: :
: : So tell me, what are the first two infinite numbers? *You
: : seem to be bursting to tell everyone how smart you are!
:
: No, I'm giving you an opportunity to show us how well you understand
: transfinite arithmetic. How can it be that one of the numbers (aleph-1) is
: larger than the other (aleph-0), given that both of them are infinite? The
: proof is actually quite simple. If you're stumped, Wikipedia must surely have
: it.
:
: : (But you do get a few points for Googling the concept, which allowed you to
: : maintain some minimal pretense of understanding. Very frankly, I didn't think
: : you would manage to do even that.)
: :
: : Your skill in judging people is unsurpassed.
: :
: :
: : BTW, in an English-speaking newsgroup, you really should refer to "aleph-one"
: : rather than "aleph-eins". (Auf Deutsch, aleph-eins ist richtig,
: : natürlich.)
: :
: : So you'd advocate "aleph-zero" in an English-speaking newsgroup,
: : too?
:
: Not necessarily (although I have heard it called that). The word "null" is
: just as understandable in English as it is in German. In the math class where
: I first encountered the number, the professor called it "aleph-null". And
: aleph-1 was referred to as "c", which stood for the "cardinal number of the
: continuum". I'm not even certain that at the time (the late 1950s) it had been
: proven that there are no other numbers between aleph-0 and c. I've since read
: that it's now known to be the case (which may account for the adoption of the
: term "aleph-1"), but I don't recall seeing the proof.
:
: Bob
:
: Why don't we just spout things that are beyond the concept of most
: camera owners?
:
: I was the National Digital Colour Specialist for Minolta, 6 years with
: Canon, 10 with Xerox.
:
: And I have no clue about what you are trying to articulate.

It's weird how far OT we sometimes manage to get. The infinity argument
started with Wolfgang ridiculing an earlier poster for something he said in a
thread about people who set off P&S flash cameras in sports arenas. My fault
for then egging Wolfgang on. Sorry.

Bob
  #32  
Old April 11th 13, 01:34 PM posted to rec.photo.digital.slr-systems
Wolfgang Weisselberg
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Posts: 5,285
Default Food for thought, camera access to events

Robert Coe wrote:
On Fri, 5 Apr 2013 22:17:01 +0200, Wolfgang Weisselberg
: Robert Coe wrote:
: On Tue, 2 Apr 2013 18:37:25 +0200, Wolfgang Weisselberg


: : I shouldn't bother, but I'm going to call your bluff. Please tell us what the
: : first two infinite numbers are


: [...]


: No, they are not sets. They are the (infinite) numbers of *members*
: incorporated in two different sets. I leapt to the conclusion that transfinite
: arithmetic is beyond your reach, and you seem to have proven me correct.


: So tell me, what are the first two infinite numbers? You
: seem to be bursting to tell everyone how smart you are!


No,


Ah, you're playing teacher.
So what are your credentials?

I'm giving you an opportunity to show us how well you understand
transfinite arithmetic. How can it be that one of the numbers (aleph-1) is
larger than the other (aleph-0), given that both of them are infinite?


countable, not countable.
Interval between *any* 2 real numbers always contains at least
one real number (a+b)/2, which by induction means they all
contain infinite real numbers.
Can't bijectively map from aleph-null to, say, interval [0-1[
in real numbers.

: BTW, in an English-speaking newsgroup, you really should refer to "aleph-one"
: rather than "aleph-eins". (Auf Deutsch, aleph-eins ist richtig,
: natürlich.)


: So you'd advocate "aleph-zero" in an English-speaking newsgroup,
: too?


Not necessarily (although I have heard it called that). The word "null" is
just as understandable in English as it is in German. In the math class where
I first encountered the number, the professor called it "aleph-null". And
aleph-1 was referred to as "c", which stood for the "cardinal number of the
continuum". I'm not even certain that at the time (the late 1950s) it had been
proven that there are no other numbers between aleph-0 and c. I've since read
that it's now known to be the case (which may account for the adoption of the
term "aleph-1"), but I don't recall seeing the proof.


Do a google on that proof and report back. That's your
opportunity to show us how well you remember transfinite
arithmetic.

-Wolfgang
 




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