A function is a set F of ordered pairs [x,y], x \in X, y \in Y, such that for all [x1,y1], [x2,y2] \in F, x1=x2 -> y1=y2.
The conventional notation for [x,y] being in F is f(x)=y. (The conventional notation for an ordered pair is angle brackets, but I hate typing HTML entities.)
Therefore the definition of a function is that it is uniquely valued everywhere it is defined, i.e. if f(x)=y, then f(x) is not z for any z!=y.
Surjections are functions such that for all y \in Y, there exists an x \in X such that [x,y] \in F.
Injections are functions such that for all [x1,y1], [x1,y2] \in Y, y1=y2 -> x1=x2
Yeah, the "moderators" should of noticed that. If they had, probably they all of the sudden would have changed their minds about moderating. I have a deep-seeded hatred for such errors, they make me loose my mind. However, moderators do have free reign.
However, attacking the intended payload due to presentation issues (inability use a pat phrase correctly) is a classic Logical Fallacy. Some people spend so little time with authoratitive written material that the correct forms may never have been seen, and only the spoken version encountered.
I'm a speed freak, everything I do needs to be fast (I work with computational number theory), but I code almost entirely in C, and only very very rarely resort to assembly language. I often end up with faster code than those that are 100% assembly language, due to investment in your #3 and #6.
And all of my house-keeping tasks (management of lists of candidates, or factors, or whatever) I code in Perl, because of your #1 (and #3).
"If you haven't seen this before and are feeling conned, try it out with other numbers"
The "proof" is in some ways nonsense. It lets you "prove" 1+2+4+8+16+.... = -1
Let S = 1+2+4+8+16+... 1+2*S = 1+(2+4+8+16+32+...) So S = 1+2*S => S = -1
The correct proof is to show that for any finite quantity, delta, the value of the expression is closer to 1 than delta. (Note, that is ambiguously worded, but English is lousy for mathematical formality.)
"sqrt(-1)" is not an equation, it is not a function of a variable, it has no roots.
sqrt(-1) doesn't even have two values, as sqrt() is a function, having a single value. There are some, who are ignorant of the foundations of maths (namely what the set-theoretical definition of a function is), who try to pretend that a "multifunction", or "multi-valued function" is a kind of function, but it is not.
There's still a Sinclair on one of the science parks in the north of Cambridge. It's just past the Milton Road Park & Ride terminus. I believe Sir Clive no longer has anything to do with it.
Gravity isn't proven in the same way as conservation of mass wasn't proven.
Presently it's only an _assumption_ that inertial mass is the same as gravitational mass. That it was an assumption was made _explicit_ to us in college. Perhaps your lectures were dumbed down a bit. We have no reason to doubt it, and therefore it's as much a postulate as anything else is in the system.
We simply have a model, which is less wrong[*] than our previous model. Prior models had as laws things like conservation of mass, which we now know to be false due to mass/energy equivalence. Prior models had ultraviolet catastrophies. Prior models had electrons as distinct particles. Prior models had no Lorenzian invariant transformations. Prior models had no Pauli exclusion principle. Prior models had no uncertainty principle.
Stop thinking that our current model is unassailable.
There are still unencountered, and thus untested, situations where our model could easily break down. C.f. the loss-of-information question categorically _not_ resolved recently.
No amount of precision will _prove_ the correctness of a theory. It will _support_, but not prove.
Theory - All pigeons are grey. No number of grey pigeons can prove that theory true as if after that number of grey pigeons has been found an albino one is seen, then the theory is disproved.
Anything which can be later disproved can not have previously be said to be proved.
I had just stopped the two jobs on the Alpha and P4, and was processing the log files from the two machines on my file-server. Once the results had been merged, I started up the Alpha again with the new dataset. Hence the ramping up of the load again.
Well spotted. Why do people with smart brains like yourself post AC?
Sure, 500 days it pretty crap. I moved a new hard disk into it last year. My main file server, if it wasn't for a power-cut 908 days ago, and my UPS blowing up with a big blue flash 602 days ago, would have an uptime of 1258 days. (i.e. 602+306+350) At one point, with the dodgy electricity here, I was sure I'd never even get 1 year uptime. As you can see - investing in a UPS never did me any good at all!
"Virginia Tech's third-fastest supercomputer in the world"
Everyone in the world who knew about supercomputing told them, at the time, that they should use proper error-correcting RAM, but oh no, the cheapskates at Virginia knew better.
And consequently they never performed any computation whose results they could be sure of the correctness of. They simply said that they'd just repeat the computation repeatedly until they got agreement. And therefore they were less than half of the speed that they claimed to be.
The embarassment was correctly ripped up and sold off for scrap, and was jetisoned from the top 500 list.
Allegedly they're going to do it properly next time.
But hey - the scrapping of the old one is a good thing, as there are hundreds of people who could pick up really nice kit pretty cheap. Those POWER-based PPCs are damn fine processors. I'd certainly have been queueing up to buy one if I were more local.
Toms Root Boot was always enough for me. 1 floppy.
TRB, Lepton and other floppy distributions I've tried (for real use, not just recovery situations) have all been exceptionally high quality. The guys who put them together really know what they're doing. Any idiot can stick half a gig of programs on a CD, it takes smarts to get them onto 1 o 2 floppies.
Slashdot Mirror
Don't mix peak with sustained.
If their peak is that much higher than the sustained, then I would suspect that their 88% measure of efficiency is not the full truth.
As you say, good to see FOSS with such a high profile.
FP.
A function is a set F of ordered pairs [x,y], x \in X, y \in Y, such that for all [x1,y1], [x2,y2] \in F, x1=x2 -> y1=y2.
The conventional notation for [x,y] being in F is f(x)=y. (The conventional notation for an ordered pair is angle brackets, but I hate typing HTML entities.)
Therefore the definition of a function is that it is uniquely valued everywhere it is defined, i.e. if f(x)=y, then f(x) is not z for any z!=y.
Surjections are functions such that for all y \in Y, there exists an x \in X such that [x,y] \in F.
Injections are functions such that for all [x1,y1], [x1,y2] \in Y, y1=y2 -> x1=x2
Bijections are surjective injections.
FP.
We have a winner!
(Actually, I use so-called scare quotes as an short-cut for "so-called".)
FP.
Re: your comment. Check your dictionary: you've conflated transcribe with transpose.
Yeah, the "moderators" should of noticed that. If they had, probably they all of the sudden would have changed their minds about moderating. I have a deep-seeded hatred for such errors, they make me loose my mind. However, moderators do have free reign.
However, attacking the intended payload due to presentation issues (inability use a pat phrase correctly) is a classic Logical Fallacy. Some people spend so little time with authoratitive written material that the correct forms may never have been seen, and only the spoken version encountered.
FP.
Brilliant post.
I'm a speed freak, everything I do needs to be fast (I work with computational number theory), but I code almost entirely in C, and only very very rarely resort to assembly language. I often end up with faster code than those that are 100% assembly language, due to investment in your #3 and #6.
And all of my house-keeping tasks (management of lists of candidates, or factors, or whatever) I code in Perl, because of your #1 (and #3).
FP.
"Disclaimer: I use Perl almost exclusively for programming."
Good, it's useless for babysitting, or cooking, for example.
FP.
"If you haven't seen this before and are feeling conned, try it out with other numbers"
The "proof" is in some ways nonsense. It lets you "prove" 1+2+4+8+16+.... = -1
Let S = 1+2+4+8+16+...
1+2*S = 1+(2+4+8+16+32+...)
So S = 1+2*S
=> S = -1
The correct proof is to show that for any finite quantity, delta, the value of the expression is closer to 1 than delta. (Note, that is ambiguously worded, but English is lousy for mathematical formality.)
FP.
That's a field of finite characteristic though.
Hmmm, actaully you knew that, I'm sure. It was probably grandparent who didn't.
FP.
"sqrt(-1) has two roots... -i and i."
Nope.
"sqrt(-1)" is not an equation, it is not a function of a variable, it has no roots.
sqrt(-1) doesn't even have two values, as sqrt() is a function, having a single value. There are some, who are ignorant of the foundations of maths (namely what the set-theoretical definition of a function is), who try to pretend that a "multifunction", or "multi-valued function" is a kind of function, but it is not.
x^2=-1 has two roots: +/-sqrt(-1)
FP.
There's still a Sinclair on one of the science parks in the north of Cambridge. It's just past the Milton Road Park & Ride terminus. I believe Sir Clive no longer has anything to do with it.
FP.
RANDOMISE USR 1234
I think 1331 was similar, but with different colours.
It's been 15 years though...
FP.
Gravity isn't proven in the same way as conservation of mass wasn't proven.
Presently it's only an _assumption_ that inertial mass is the same as gravitational mass. That it was an assumption was made _explicit_ to us in college. Perhaps your lectures were dumbed down a bit. We have no reason to doubt it, and therefore it's as much a postulate as anything else is in the system.
We simply have a model, which is less wrong[*] than our previous model. Prior models had as laws things like conservation of mass, which we now know to be false due to mass/energy equivalence. Prior models had ultraviolet catastrophies. Prior models had electrons as distinct particles. Prior models had no Lorenzian invariant transformations.
Prior models had no Pauli exclusion principle. Prior models had no uncertainty principle.
Stop thinking that our current model is unassailable.
There are still unencountered, and thus untested, situations where our model could easily break down. C.f. the loss-of-information question categorically _not_ resolved recently.
FP.
* - Stephen Hawking's words, not mine.
Just give me a yes or a no -
are Javascript programs, Perl programs, Java programs, and Basic programs just "data"?
Everything you've said so far leads me to believe that your only consistent answer would be "yes".
I'm in my third decade as a developer.
FP.
No amount of precision will _prove_ the correctness of a theory. It will _support_, but not prove.
Theory - All pigeons are grey.
No number of grey pigeons can prove that theory true as if after that number of grey pigeons has been found an albino one is seen, then the theory is disproved.
Anything which can be later disproved can not have previously be said to be proved.
FP.
Unless this preliminary result is the output of a cynical publish-or-perish mentality.
Who would the resources to shoot this down if it were to be fraudulent? How long did Mendel yet away with his faked results? Exactly.
FP.
Pencils fill the confined atmosphere with graphite dust. You don't want layers of graphite on your circuit boards.
They US/SU should both have just used either wax crayons, or etchasketch.
FP.
Ditto. Young female driver ~20; I was on a pedal bike. Middle of a bright day.
Got any refs for your Hertz rental return anecdote above? No obvious google queries pick it up. Sounds like a fun tale.
FP.
In that case, you should bow out of the argument now, before you embarass yourself further.
Postscript is a language very closely related to Forth. It's no more data than Java, Perl, Basic, JavaScript code are.
FP
So, is a postscript document data or code?
FP.
It's big enough to display
+--------+
|watching|
| porno |
+--------+
Oh, you wanted non-obvious. My mistake.
FP
I had just stopped the two jobs on the Alpha and P4, and was processing the log files from the two machines on my file-server. Once the results had been merged, I started up the Alpha again with the new dataset. Hence the ramping up of the load again.
Well spotted. Why do people with smart brains like yourself post AC?
Sure, 500 days it pretty crap. I moved a new hard disk into it last year. My main file server, if it wasn't for a power-cut 908 days ago, and my UPS blowing up with a big blue flash 602 days ago, would have an uptime of 1258 days. (i.e. 602+306+350) At one point, with the dodgy electricity here, I was sure I'd never even get 1 year uptime. As you can see - investing in a UPS never did me any good at all!
FP.
It's not a bug, it's simply part of the design. It's a 32-bit jiffy counter, and therefore wraps at 497 days.
/var/log/dmesg
Witness:
phil@kilospaz:phil$ uptime
11:47:49 up 105 days, 23:18, 11 users, load average: 1.00, 1.00, 1.00
Which is _602_ days uptime, as can be verified from:
phil@kilospaz:phil$ stat
File: "/var/log/dmesg"
Size: 3063 Blocks: 6 IO Block: 4096 Regular File
Device: 303h/771d Inode: 10090 Links: 1
Access: (0644/-rw-r--r--) Uid: ( 0/ root) Gid: ( 0/ root)
Access: Mon Jul 5 17:47:33 2004
Modify: Fri Feb 21 08:32:18 2003
Change: Fri Feb 21 08:32:18 2003
Yes, yes, yes, uptime is a subsitute for penis length, I know.
FP.
"Virginia Tech's third-fastest supercomputer in the world"
Everyone in the world who knew about supercomputing told them, at the time, that they should use proper error-correcting RAM, but oh no, the cheapskates at Virginia knew better.
And consequently they never performed any computation whose results they could be sure of the correctness of. They simply said that they'd just repeat the computation repeatedly until they got agreement. And therefore they were less than half of the speed that they claimed to be.
The embarassment was correctly ripped up and sold off for scrap, and was jetisoned from the top 500 list.
Allegedly they're going to do it properly next time.
But hey - the scrapping of the old one is a good thing, as there are hundreds of people who could pick up really nice kit pretty cheap. Those POWER-based PPCs are damn fine processors. I'd certainly have been queueing up to buy one if I were more local.
FP.
Toms Root Boot was always enough for me.
1 floppy.
TRB, Lepton and other floppy distributions I've tried (for real use, not just recovery situations) have all been exceptionally high quality. The guys who put them together really know what they're doing. Any idiot can stick half a gig of programs on a CD, it takes smarts to get them onto 1 o 2 floppies.
FP.