The general rule is that one capitalises names used in apposition to the noun they qualify, so Banach algebra, Cauchy sequence, Galois group etc., but adjectives based on proper names are not capitalised. So cartesian plane, noetherian ring, abelian group.
And 'abelian group' seems certainly more common. I personally would never use 'commutative' of the additive group of a ring, for instance.
Has more-or-less everything to do with prime numbers, as you know well (vide unique factorisation of ideals in Dedekind Domains, for instance). Of course, you're completely correct about primes in Z. I was just rambling.
Also, those names are a really easy way of keeping track of the various results. Which is easier to remember 'Proposition 4.13' or 'Swan's Theorem'? Compare 'The generalised result on patching finitely present modules' or 'Quillen's Patching Theorem'?
In a very peculiar sense, it is. The reason being that by '2' we mean not only '2' but the numbers {..., -4, -2, 0, 2, 4, 6,...} (i.e. all multiples of '2'). Now we say a number, a, is a prime if the following holds: a divides xy if and only if a divides x or a divides y. A quick check shows that the prime numbers are 0, 2, 3,5,7,11,... and -2,-3,-5, -7, -11, -13...
Now, I'm not suggesting that this is the 'correct' definition of primeness, but it is how the word is generally understood in commutative ring theory. One might say that 0 is a trivial prime.
The cases of Fermat Primes, Mersenne Primes (and therefore even perfect numbers) and of Odd Perfect Numbers are still unsolved, to the best of my knowledge.
Also, of course, there are many well-known diophantine equations (such as n^3 - m^2 -2 = 0) that have finitely many solutions.
I suppose the most striking example of 'unexpected finiteness' is the orders of sporadic groups (see mathworld.wolfram.com). These are finite groups which have no normal proper subgroups (so their structure is essentially 'irreducible') but they do not fall into any established category of simple group. The largest of these groups are staggeringly huge, but there are only 26. Why this is so is a complete mystery to me.
In 'caveat emptor', the verb is in the active mood, so the emptor is being beware. In caveatur paypal, the verb is in the passive, so the subject (paypal) is suffering the being beware (by whom paypal is being beware is left unspecified).
So 'caveatur paypal' should mean, roughly, 'one should beware of paypal'. Of course, this trnaslation is poor because there is no transitive verb in english with a direct object to translate cavere. But not to worry.
There should be an immediarte undelete command. Or better still, disk space permitting, an undelete command that worked for a certain period after the original rm.
Does anyone else wonder what it might mean when a company as massively gigantically ginormous as Microsoft can't churn out a new release of a flagship program in a year or two? They are either doing something exceptionally cunning and devious or else they simply can't make a new version in this space of time, and I'm sure we all go with option b.
I just think it means personal computers are now officially insane.
...University? Anyone else less than convinced by this scenario? Sounds like Americans are so crazy, they'd suspect anyone. Hey I have a bomb...... and a big hello to my new FBI fans and admirers, xx ben.
I tried starting three web browsers on this machine (MacOS X 10.3, 256MB RAM, 933 MHz G4 iBook). Just for laughs. Internet Explorer 5.2 -- 5 seconds Firefox 0.8 -- 6 seconds Safari 1.2.1 -- 11 seconds
What does this tell me? More or less nothing, because, in the first place, I only start a browser once a day, if that. In the second, Firefox has bugs and IE just doesn't do tabs. So, frankly, load time isn't important.
And while I was at it, I made them all display a series of miscelaneous sites. Safari shaves seconds off the time the other two take. So I guess load time REALLY DOESN'T MATTER.
That's not quite how the law works, as a rule. If the employers are seen to be making a reasonable attempt to filter obscene spam, then that should suffice. I do agree though that employers have a duty to ensure that their employees are not pissed off by circumstances they can easily mitigate. Think of it as similar to installing air-conditioning; it's not perfect, and it may not _strictly speaking_ be necessary in all cases, but it's certainly a good thing for employees.
If this makes employers consider better spam-filtering mechanisms, surely that's a good thing for everyone. We know that it is more-or-less impossible to stem spam at the source, so legislating to impede spam at some other point is not entirely a bad thing.
Of course, the tinfoil-hat folks will be vomiting to themselves over the evil intrusive regulation, but come on, how hard is it to try to filter spam?
Slashdot Mirror
The general rule is that one capitalises names used in apposition to the noun they qualify, so Banach algebra, Cauchy sequence, Galois group etc., but adjectives based on proper names are not capitalised. So cartesian plane, noetherian ring, abelian group.
And 'abelian group' seems certainly more common. I personally would never use 'commutative' of the additive group of a ring, for instance.
Has more-or-less everything to do with prime numbers, as you know well (vide unique factorisation of ideals in Dedekind Domains, for instance). Of course, you're completely correct about primes in Z. I was just rambling.
Also, those names are a really easy way of keeping track of the various results. Which is easier to remember 'Proposition 4.13' or 'Swan's Theorem'? Compare 'The generalised result on patching finitely present modules' or 'Quillen's Patching Theorem'?
In a very peculiar sense, it is. The reason being that by '2' we mean not only '2' but the numbers { ..., -4, -2, 0, 2, 4, 6,...} (i.e. all multiples of '2'). Now we say a number, a, is a prime if the following holds: a divides xy if and only if a divides x or a divides y. A quick check shows that the prime numbers are 0, 2, 3,5,7,11,... and -2,-3,-5, -7, -11, -13...
Now, I'm not suggesting that this is the 'correct' definition of primeness, but it is how the word is generally understood in commutative ring theory. One might say that 0 is a trivial prime.
the function
... + x (x times)
f(x) = x +
is defined only as f:N -> N . One cannot differentiate this function (it's not defined on a Banach space). You try to do this in line 2.
Also, of course, there are many well-known diophantine equations (such as n^3 - m^2 -2 = 0) that have finitely many solutions.
I suppose the most striking example of 'unexpected finiteness' is the orders of sporadic groups (see mathworld.wolfram.com). These are finite groups which have no normal proper subgroups (so their structure is essentially 'irreducible') but they do not fall into any established category of simple group. The largest of these groups are staggeringly huge, but there are only 26. Why this is so is a complete mystery to me.
That's a personal favourite.
I don't see your point.
In 'caveat emptor', the verb is in the active mood, so the emptor is being beware. In caveatur paypal, the verb is in the passive, so the subject (paypal) is suffering the being beware (by whom paypal is being beware is left unspecified).
So 'caveatur paypal' should mean, roughly, 'one should beware of paypal'. Of course, this trnaslation is poor because there is no transitive verb in english with a direct object to translate cavere. But not to worry.
yes, or you can hit the 'esc' key or something. Always works for me (G4 iBook though, so ymmv).
wants to retain its amateur status so it can compete in the olympics.
I'm sure it can make its costs back in sponsorship though.
Surely `caveatur paypal' (i.e. passive subjunctive)
microsoft patented apples.
Since I don't enjoy looking stupid, I'll wait for metal shoelaces, thank you very much.
There should be an immediarte undelete command. Or better still, disk space permitting, an undelete command that worked for a certain period after the original rm.
I know I'd have killed for one in the past.
If we voted for Cthulhu, it'd be everyone.
There's a thought.
Does anyone else wonder what it might mean when a company as massively gigantically ginormous as Microsoft can't churn out a new release of a flagship program in a year or two? They are either doing something exceptionally cunning and devious or else they simply can't make a new version in this space of time, and I'm sure we all go with option b.
I just think it means personal computers are now officially insane.
...University? Anyone else less than convinced by this scenario? Sounds like Americans are so crazy, they'd suspect anyone. Hey I have a bomb... ... and a big hello to my new FBI fans and admirers,
xx ben.
the music on the radio sounds worse every year?
I tried starting three web browsers on this machine (MacOS X 10.3, 256MB RAM, 933 MHz G4 iBook). Just for laughs.
Internet Explorer 5.2 -- 5 seconds
Firefox 0.8 -- 6 seconds
Safari 1.2.1 -- 11 seconds
What does this tell me? More or less nothing, because, in the first place, I only start a browser once a day, if that. In the second, Firefox has bugs and IE just doesn't do tabs. So, frankly, load time isn't important.
And while I was at it, I made them all display a series of miscelaneous sites. Safari shaves seconds off the time the other two take. So I guess load time REALLY DOESN'T MATTER.
That's not quite how the law works, as a rule. If the employers are seen to be making a reasonable attempt to filter obscene spam, then that should suffice. I do agree though that employers have a duty to ensure that their employees are not pissed off by circumstances they can easily mitigate. Think of it as similar to installing air-conditioning; it's not perfect, and it may not _strictly speaking_ be necessary in all cases, but it's certainly a good thing for employees.
If this makes employers consider better spam-filtering mechanisms, surely that's a good thing for everyone. We know that it is more-or-less impossible to stem spam at the source, so legislating to impede spam at some other point is not entirely a bad thing.
Of course, the tinfoil-hat folks will be vomiting to themselves over the evil intrusive regulation, but come on, how hard is it to try to filter spam?
...Linux Linux Linux Linux Linux Linux Linux Linux Linux Linux LicENSE! LicENSE!
Aaah Sun!
Repeat forever
The colonies, sir, are part of the Empire.
The next Robocop is going to be very slow
On a mac, you can install it three times!
I have emacs installed by default by the OS,
I have Carbon Emacs,
I have XEmacs.
And I use them all to play tetris.