His thesis would have demanded more critical examination than a research paper. So i think it's fair to say that he earned that pHD
This is a fairly incredible assertion. At least in mathematics, a thesis, once completed, is buried far away from the eyes of all but the most interested, the only scrutiny through which it has had to go being that of two readers, one of whom usually skims it and issues a perfunctory `I agree with the primary reader'. A paper, however, has to go through a review process -- which admittedly can let through its share of flaws -- and, once it has done so, is readily available to, and frequently checked by, the (mathematical) public. I would say a published paper, at least eventually, undergoes far more scrutiny (which is not to say, obviously, that it's got to be correct either!).
If it is played 40 times a week people are going to hear it and *believe* that it is popular. When it gets artificially vaulted to the top of the charts more people are going to *believe* that it is popular.
Aside from the obvious automatic `rich corporations = evil', I can't seem to get as outraged about this issue as apparently I should. I especially can't manage to get worked up about the point raised in the parent post -- what ill consequences will follow if people believe a song is more popular than it is? Maybe they'll buy crap, but if they're basing their music-buying decisions solely on what's popular (legitimately or otherwise) they would have bought crap anyway.
No one has an intrinsic right to drive a car, but everyone has a right to pay to drive a car. Public transportation is a great solution, if you can get to it. I work in Chicago and my wife works out in Rockford (about 90 miles apart); my university is not in Rockford and my wife's company has no presence in Chicago, so at least one of us has to make a long commute, and there's no way to get to Rockford purely by public transportation. Paying the $100 cab fare to the nearest train station daily is also not a reasonable option. If a train or bus ran within any feasible distance -- walking, biking, whatever -- I would be delighted to get rid of my car, but I don't have that option; so surely I at least have the right to pay the fees to provide myself transportation that no one else will!
This is a puzzling statement -- it's false unless a + b = 0 or c = 1. Maybe you meant the right-hand side to be ((a + b)c)/c, or something? In any case, the distributive law as stated tells you only about multiplication. To get a statement about division, you have to divide, which is an illegitimate operation if the putative divisor is 0.
This is, of course, the lesson of Abu Ghraib: You can get any statement you want if you use illegal techniques.
I don't have any problem with the distributive law (I used it myself in my argument). I was bothered by the assumption that 1 x 0 = 0 until I reflected (just now) that 1 is a multiplicative identity, so the statement is beyond reproach. Sorry. (Correction, that is, humbly withdrawn by the relevant smart arse.)
In fact de Branges himself, as the article mentions, has tried this before; I'm pretty sure that a few years ago he also announced a proof (which turned out to be wrong).
Besides, any integer (greater than 1) raised to the power of three cannot possibly be a prime number.
No integer cubed is a prime number: Neither 1 nor 0 is prime. (Imagine what would happen to unique factorisation if 1 were a prime number....) Accordingly, sadly, the smallest such number is 10 = 3 + 7 = 5 + 5.
1. Read every contract you sign, even the fine print, even the one at Blockbuster Video. The folks in line behind you can deal with it and might learn something.
I was brought up well and have always made this a practice. You can imagine my shock when, upon asking Verizon for a copy of the cell phone contract before I signed (on one of those loathsome electronic signing-pads), I was told that the system was set up so that they couldn't print out a copy until I signed!
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This is a fairly incredible assertion. At least in mathematics, a thesis, once completed, is buried far away from the eyes of all but the most interested, the only scrutiny through which it has had to go being that of two readers, one of whom usually skims it and issues a perfunctory `I agree with the primary reader'. A paper, however, has to go through a review process -- which admittedly can let through its share of flaws -- and, once it has done so, is readily available to, and frequently checked by, the (mathematical) public. I would say a published paper, at least eventually, undergoes far more scrutiny (which is not to say, obviously, that it's got to be correct either!).
Aside from the obvious automatic `rich corporations = evil', I can't seem to get as outraged about this issue as apparently I should. I especially can't manage to get worked up about the point raised in the parent post -- what ill consequences will follow if people believe a song is more popular than it is? Maybe they'll buy crap, but if they're basing their music-buying decisions solely on what's popular (legitimately or otherwise) they would have bought crap anyway.
No one has an intrinsic right to drive a car, but everyone has a right to pay to drive a car. Public transportation is a great solution, if you can get to it. I work in Chicago and my wife works out in Rockford (about 90 miles apart); my university is not in Rockford and my wife's company has no presence in Chicago, so at least one of us has to make a long commute, and there's no way to get to Rockford purely by public transportation. Paying the $100 cab fare to the nearest train station daily is also not a reasonable option. If a train or bus ran within any feasible distance -- walking, biking, whatever -- I would be delighted to get rid of my car, but I don't have that option; so surely I at least have the right to pay the fees to provide myself transportation that no one else will!
This is a puzzling statement -- it's false unless a + b = 0 or c = 1. Maybe you meant the right-hand side to be ((a + b)c)/c, or something? In any case, the distributive law as stated tells you only about multiplication. To get a statement about division, you have to divide, which is an illegitimate operation if the putative divisor is 0.
This is, of course, the lesson of Abu Ghraib: You can get any statement you want if you use illegal techniques.
I don't have any problem with the distributive law (I used it myself in my argument). I was bothered by the assumption that 1 x 0 = 0 until I reflected (just now) that 1 is a multiplicative identity, so the statement is beyond reproach. Sorry. (Correction, that is, humbly withdrawn by the relevant smart arse.)
In fact de Branges himself, as the article mentions, has tried this before; I'm pretty sure that a few years ago he also announced a proof (which turned out to be wrong).
This is fine as a proof that 0 x 0 = 0 once you know that 1 x 0 = 0. The proof (of either) is roughly as in your second and third lines:
a x 0 = a x (0 + 0) = a x 0 + a x 0
Cancelling a x 0 from both sides (which we may do, since we're in a group) gives a x 0 = 0.
No integer cubed is a prime number: Neither 1 nor 0 is prime. (Imagine what would happen to unique factorisation if 1 were a prime number ....) Accordingly, sadly, the smallest such number is 10 = 3 + 7 = 5 + 5.
Boy, I'd like to reverse that right.
I was brought up well and have always made this a practice. You can imagine my shock when, upon asking Verizon for a copy of the cell phone contract before I signed (on one of those loathsome electronic signing-pads), I was told that the system was set up so that they couldn't print out a copy until I signed!