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#31




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 (aleph1) is : larger than the other (aleph0), 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 Englishspeaking newsgroup, you really should refer to "alephone" : : rather than "alepheins". (Auf Deutsch, alepheins ist richtig, : : natürlich.) : : : : So you'd advocate "alephzero" in an Englishspeaking 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 "alephnull". And : aleph1 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 aleph0 and c. I've since read : that it's now known to be the case (which may account for the adoption of the : term "aleph1"), 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




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 (aleph1) is larger than the other (aleph0), 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 alephnull to, say, interval [01[ in real numbers. : BTW, in an Englishspeaking newsgroup, you really should refer to "alephone" : rather than "alepheins". (Auf Deutsch, alepheins ist richtig, : natÃ¼rlich.) : So you'd advocate "alephzero" in an Englishspeaking 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 "alephnull". And aleph1 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 aleph0 and c. I've since read that it's now known to be the case (which may account for the adoption of the term "aleph1"), 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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