Mathematicians aren't sloppy like that. There is a careful distinction made between "discrete numbers" (basically natural numbers; there's a & b different but with no other number in between them) and "continuous numbers" (basically real or infinite decimal numbers; for any a & b different, there's always some other number in between them). In fact, the two give rise to complete separate branches of mathematics.
Here is an article on decimal representation. 1 has another infinite decimal expansion, i.e., 1 = 1.000.... 1/3 also has an infinite decimal expansion, i.e., 0.3333... So perhaps you would conclude that no multiplication can be accomplished on these numbers, either.
The solution to your paradox is that there are every-so-slightly more sophisticated mathematical techniques for getting multiplication done than mechanically multiplying each digit (for example, if you know that all subsequent digits are a particular fixed digit or a repeating pattern).
Here is an article on decimal representation. By definition, it's equivalent to saying r = a0.a1a2a3a4... (all the digits). Every digit is placed at a specific location that can be identified with an integer index n, i.e., a(n). There is no upper bound to what the index n can be (that's what the infinity symbol is defined to mean here).
So I challenge you to identify the integer index (n) at which the proposed "1" is placed.
"Surely the problem is that you're assuming sqrt(1) = 1 when actually it is +- 1?"
False. The symbol sqrt() (radical) is defined to be the principal (positive) square root only. For example: sqrt(1) = 1 (not +/-1).
You've confused this with the separate issue that an equation of form x^2 = n will have two solutions, which can be found by (1) finding the sqrt() of both sides, and (2) inserting a +/- symbol. For example: x^2 = 1 implies x = +/-sqrt(1) implies x = +/-1.
You're missing the interesting point that most people don't see: Even just restricting yourself purely to decimal-point expansions, some numbers have 2 representations (specifically, any terminating decimal). In other words, decimal representations are not 1-to-1 (assuming infinite expansions are legitimate), whereas most people expect the opposite.
You could call them "idiots" or you could call them "tyrants with a limited fief".
They're entirely accustomed to making outrageous demands and having others bend over immediately. Heck, this could be an opening salvo before lobbying the legislature to make it mandatory, no compensation to Google.
Suggest you try it. Got my account in January, and quite pleased with how elegant and lightweight it is, how little time it takes, and how it fits into my lifestyle. It honestly makes me happy to get little blurbs from friends I haven't seen in a while, doing cool things with their families. Yesterday I saw friends planning to go to some local rock shows next week I didn't know about, maybe I'll go meet up with them there. Wouldn't have been efficient for them to email or phone about stuff like that, as I assume the response rate would be too low.
I'm also kind of pleased that Facebook serves as a "honeypot" for people with personality disorders. If they're a whack job, it comes out fast, and I can de-friend them and move on. One "friend" went so crazy he added 800 friends and every app he could find, spent all day on it, self-imploded, and had to delete his account. It's a robust, self-correcting system.
This goes for any one in an advising capacity: get the person to at least think about (ideally investigate) lifestyle of the job, like compensation, work hours, length of career, level of autonomy and self-direction, etc. Ideally go on premises for at least a single day.
One of the best things I ever did is work on a feature movie set handling animals for a few weeks. Wiped the idea of film school out of my head right quick.
Disagree. Worked several game jobs and have many friends in the industry. Pay for programmers is fairly high. But you'll be working ~100 hour weeks for it. So on an hourly basis (and more generally, life-commitment), it's fairly low compensation.
This sounds like all the other wordy nonsensical bullshit people use to justify running headlong into financial debt crises like the mortgage meltdown, etc.
I suggest that's an engineer-centric point of view. There's also people who (a) use problems as a point of marketing/selling/provocation (without ever fixing them), and (b) invent/mythologize brand new problems for like purpose.
Do this whole operation 3,000-fold, and then increase taxes by a like amount ($3000 per U.S. resident each year), and at that point you've got basically a balanced federal budget. i.e., The $13 trillion national debt holds steady instead of growing more.
"As long as those ISPs follow the law regarding the disclosure of this personal data, I have nothing against it... Of course ISPs should only disclose personal data when the law requires them to do so."
Those are likely two very different things. If the law is "do whatever you want with customer data" (or equivalently, simply silent on the issue), then you can be releasing data without any "requirement" and still following the law.
But then maybe I've got a U.S.-biased perspective.
Good question. I'm old enough that I'm in the habit of downloading my info every month (i.e., part of my monthly former balance checkbook/ pay bills by hand process), so it hadn't occurred to wonder how far back it goes.
I use NYCB (New York Community Bank) here in NYC. Turns out I can download stuff from the past 6 months, and it's free. Things I'm not thrilled about with the system: (1) Got hung up when I first applied for online access because they demanded my mother's birthdate and I actually don't know it. (Friendly girls at bank laughed and said "make something up", but I'm aware of banking fine-print gotchas). (2) The online site demands a ridiculous amount of personal info, requiring a new trio of "security questions" every 3 months or so (Mom's name, dad's name, pet's name, street, college professor, best man, etc., etc. -- I just fill in random codes but now have a list 11 items long). (3) Message system spams me with sales pitch for online bill pay every 6 weeks or so.
"This only holds if the union doesn't provide enough benefit to stop people from wanting to break ranks."
Short-term benefits (e.g., one person looking for a job today) and long-terms benefits (e.g., median industry salary for the next decade) may differ. It's a bit like a war in which some sacrifices must be made. "United we stand, divided we fall," and all that. (Or, "Needs of the many etc." if you're a Star Trek fan.)
Slashdot Mirror
LOL, really hard.
"but .999... is not a rational number, it's a real number."
Also, Snowball is not a cat, she's a mammal.
Also, as my mother said, "We're not Methodists, we're Christians".
Mathematicians aren't sloppy like that. There is a careful distinction made between "discrete numbers" (basically natural numbers; there's a & b different but with no other number in between them) and "continuous numbers" (basically real or infinite decimal numbers; for any a & b different, there's always some other number in between them). In fact, the two give rise to complete separate branches of mathematics.
Here is an article on decimal representation. 1 has another infinite decimal expansion, i.e., 1 = 1.000.... 1/3 also has an infinite decimal expansion, i.e., 0.3333... So perhaps you would conclude that no multiplication can be accomplished on these numbers, either.
The solution to your paradox is that there are every-so-slightly more sophisticated mathematical techniques for getting multiplication done than mechanically multiplying each digit (for example, if you know that all subsequent digits are a particular fixed digit or a repeating pattern).
Here is an article on decimal representation. By definition, it's equivalent to saying r = a0.a1a2a3a4... (all the digits). Every digit is placed at a specific location that can be identified with an integer index n, i.e., a(n). There is no upper bound to what the index n can be (that's what the infinity symbol is defined to mean here).
So I challenge you to identify the integer index (n) at which the proposed "1" is placed.
That's not "after infinity", that's "larger than infinity" (crudely speaking).
Most people already know there are many different-but-equivalent ways to write a fraction.
Most people do not know that there can be multiple different-but-equivalent ways to write a decimal.
That's the point.
"Surely the problem is that you're assuming sqrt(1) = 1 when actually it is +- 1?"
False. The symbol sqrt() (radical) is defined to be the principal (positive) square root only. For example: sqrt(1) = 1 (not +/-1).
You've confused this with the separate issue that an equation of form x^2 = n will have two solutions, which can be found by (1) finding the sqrt() of both sides, and (2) inserting a +/- symbol. For example: x^2 = 1 implies x = +/-sqrt(1) implies x = +/-1.
You're missing the interesting point that most people don't see: Even just restricting yourself purely to decimal-point expansions, some numbers have 2 representations (specifically, any terminating decimal). In other words, decimal representations are not 1-to-1 (assuming infinite expansions are legitimate), whereas most people expect the opposite.
You could call them "idiots" or you could call them "tyrants with a limited fief".
They're entirely accustomed to making outrageous demands and having others bend over immediately. Heck, this could be an opening salvo before lobbying the legislature to make it mandatory, no compensation to Google.
+ programmer's benefits (health, etc.; ~doubles salary)
TFA: "[A former FBI agent] said he was certain that agents who installed it would have obtained a 30-day warrant for its use."
Don't believe it. No evidence to back up claim, and source has conflict of interest.
So get a warrant.
Also: Don't believe it. Call the fucking lawyer.
Suggest you try it. Got my account in January, and quite pleased with how elegant and lightweight it is, how little time it takes, and how it fits into my lifestyle. It honestly makes me happy to get little blurbs from friends I haven't seen in a while, doing cool things with their families. Yesterday I saw friends planning to go to some local rock shows next week I didn't know about, maybe I'll go meet up with them there. Wouldn't have been efficient for them to email or phone about stuff like that, as I assume the response rate would be too low.
I'm also kind of pleased that Facebook serves as a "honeypot" for people with personality disorders. If they're a whack job, it comes out fast, and I can de-friend them and move on. One "friend" went so crazy he added 800 friends and every app he could find, spent all day on it, self-imploded, and had to delete his account. It's a robust, self-correcting system.
And that's why the more affluent folk contribute lots of money to groups who do TV advertising to convince this guy otherwise. Net profit.
This goes for any one in an advising capacity: get the person to at least think about (ideally investigate) lifestyle of the job, like compensation, work hours, length of career, level of autonomy and self-direction, etc. Ideally go on premises for at least a single day.
One of the best things I ever did is work on a feature movie set handling animals for a few weeks. Wiped the idea of film school out of my head right quick.
Disagree. Worked several game jobs and have many friends in the industry. Pay for programmers is fairly high. But you'll be working ~100 hour weeks for it. So on an hourly basis (and more generally, life-commitment), it's fairly low compensation.
This sounds like all the other wordy nonsensical bullshit people use to justify running headlong into financial debt crises like the mortgage meltdown, etc.
I suggest that's an engineer-centric point of view. There's also people who (a) use problems as a point of marketing/selling/provocation (without ever fixing them), and (b) invent/mythologize brand new problems for like purpose.
Do this whole operation 3,000-fold, and then increase taxes by a like amount ($3000 per U.S. resident each year), and at that point you've got basically a balanced federal budget. i.e., The $13 trillion national debt holds steady instead of growing more.
"As long as those ISPs follow the law regarding the disclosure of this personal data, I have nothing against it...
Of course ISPs should only disclose personal data when the law requires them to do so."
Those are likely two very different things. If the law is "do whatever you want with customer data" (or equivalently, simply silent on the issue), then you can be releasing data without any "requirement" and still following the law.
But then maybe I've got a U.S.-biased perspective.
p = 0.56? Good grief, that means that there's some (very small) evidence that the exact opposite is true.
Good question. I'm old enough that I'm in the habit of downloading my info every month (i.e., part of my monthly former balance checkbook/ pay bills by hand process), so it hadn't occurred to wonder how far back it goes.
I use NYCB (New York Community Bank) here in NYC. Turns out I can download stuff from the past 6 months, and it's free. Things I'm not thrilled about with the system: (1) Got hung up when I first applied for online access because they demanded my mother's birthdate and I actually don't know it. (Friendly girls at bank laughed and said "make something up", but I'm aware of banking fine-print gotchas). (2) The online site demands a ridiculous amount of personal info, requiring a new trio of "security questions" every 3 months or so (Mom's name, dad's name, pet's name, street, college professor, best man, etc., etc. -- I just fill in random codes but now have a list 11 items long). (3) Message system spams me with sales pitch for online bill pay every 6 weeks or so.
"This only holds if the union doesn't provide enough benefit to stop people from wanting to break ranks."
Short-term benefits (e.g., one person looking for a job today) and long-terms benefits (e.g., median industry salary for the next decade) may differ. It's a bit like a war in which some sacrifices must be made. "United we stand, divided we fall," and all that. (Or, "Needs of the many etc." if you're a Star Trek fan.)