There are several well known proofs that division by 0 is undefined, such as treating division as multiplication by the multiplicative inverse, much as addition as adding the additive inverse, which I mentioned above. If you are partial to calculus (actually, this is precalc-level stuff), another relatively straightforward proof is to consider the limit of division by some number x as x approaches 0 from the positive side vs division by x as x approaches 0 from the negative side. The two limits both have a magnitude of infinity, but are of opposite sign. This means that there is a discontinuity in division by 0, and because there are no mitigating factors in a division operation that suggests that only one of the limits would actually be correct at that value, mathematically it is undefined. For the case of 0/0, consider that the limit of 0/x as x approaches 0 is quite well defined, being 0, and the limit of x/x as x approaches 0 is also well defined, being 1. However, again there are no mitigating factors that suggest only one of these limits would be correct, so this means that you still have a discontinuity at 0, and in absence of any particular reason to choose one limit over the other at 0, that means that expression is undefined as well.
No... the post that RackinFrackin replied to was factually wrong. A number divided by 0 is *NOT* defined as either plus or minus infinity. The definition of division is such that any division by a number is equivalent to multiplying by that number's multiplicative inverse, but 0 does not have such an inverse, so dividing by 0 is like trying to multiply by a number that doesn't even exist.
In other words, it's undefined. Nothing more, and nothing less.
Division doesn't really exist in the sense of a mathematical operatoin. Division is best thought of as a convenient shorthand for multiplication by the multiplicative inverse of a number. The multiplicative inverse of a number is well defined to be such that a number multiplied by its multiplicative inverse equals the multiplicative identity value, which is 1. There is no number that can be multiplied by zero to get a value of 1, however, so "dividing by zero" is like trying to multiply by a number that doesn't exist in the first place.
Bill C51 is particularly troubling... it has already been passed into law and as such may prove very difficult to get rid of by any later prime minister that disagrees with it without a majority government.
The most particularly troubling aspect of C51 is that it empowers CSIS to break almost *ANY* law... short of inflicting enduring physical bodily harm on someone, or acts of sexual violation... in the course of disrupting anything that they believe, rightly or wrongly, to be a terrorist threat, including violating even civil and constitutional rights. That means they can imprison people because of their race, or simply because of what that person believes, for example, even if that person has done absolutely nothing wrong. if CSIS has any reason at all to suspect that such factors link them to committing any act that corresponds with a terrorist threat, a phrase that by itself is so loosely defined (in fact, it isn't even defined in this law... in fact, it appears almost intentional to have left it undefined so that CSIS could apply the term as they saw fit), that even picketing or almost any other form of entirely peaceful assembly that might happens to disrupt some activity that the government is wanting to push forward could qualify.
It's interesting to consider, however, that because CSIS also outlaws the the distribution of terrorist propoganda, if, for example, Westboro Baptist Church were Canadian, then by Bill-C51, the government would have to ban the Christian bible, since WBC uses that text to justify many of their insane acts, and the bill explicitly outlaws the dissemination of literature that encourages acts of terrorism.
... tying something you physically possess to identification, but it should never be used standalone. A password, pass-phrase, or even a pin should still be required, because anything else can always potentially be taken from you, or worse yet... compromised. The additional factor of having some physical device that can further confirm your identity gives an added layer of security over the password by itself that can still be beneficial, but it should never be trusted to the exclusion of a password.
Of so, they are independent contractors, to the best of my understanding.
If one is an employee, then they are subject to things like minimum wage laws, which requires at least some participation by the employer to affect what hours the employee works.
Actually, he patterned the file system after Minux, not Multix. He did not use any Minux code.
While what Linux would ultimately become was certainly not built entirely from scratch, particularly after the GNU tools started getting bundled with it, Linus most definitely *DID* start from scratch.
So given a choice between both the poor and the rich being taxed or the poor simply starving to death because what they could allegedly otherwise afford to feed themselves isn't available, you'd run with the latter?
I think your history is a little revisionist. Linus didn't start from scratch
Actually, yes he did... unless you have a definition of "from scratch" that is so absurdly overbroad to the point that the expression no longer carries any meaning.
True... but in the long term, the net effect is still positive... you cut down on the number of people that consume the product. Only a moderate level of enforcement, that is where it happens to be detected through procedures that are already occurring, would be required to be effective in the long run.
But the point you make prompts the question: why is the FDA banning transfat and not banning cigarettes, which have a much longer track record of causing health problems?
If the tax is sufficiently high, then in practice, the people who will consume it the most will tend to be richer... and can generally more readily afford to pay for any of the extra health care they may need because of a poor diet.
As a side effect, it also offers a revenue stream.
Actually, if an employee is smart about things, they will keep a really solid paper trail of what has been happening that leads up to their actual resignation. There are limits to what an employer is permitted to do that does not qualify as what is termed "constructive dismissal", and an employee who is on the ball when things start to heat up at work can still qualify for unemployment benefits even if they quit, if they can clearly document the circumstances behind it, and it can be shown that the employer was evidently deliberately doing things to try and get the employee to quit. It requires, however, that every incident needs to be meticulously logged, with dates, times, names of people that were involved, and where the incident occurred (on the phone, on the job site, or what have you). If you are good enough at keeping records, it shouldn't even require any real collaboration by the employer, because you will have enough documentation that the incidents can be verified independently (if one of the incidents involved changed your shift on you without giving you enough notice, for instance, you can show the logs on your cell phone records indicating exactly when they had called, leaving you inadequate time, as just one example).
Only if you measure reward by monetary gain. A pretty shallow standard, actually... you need money to live, obviously, but beyond that, your time is much more wisely invested in doing what you love. If you love philospy study philosophy.... for what it's worth, there are applications of philosophy to computer science anyways.
But trying to maximize monetary profit is a senseless goal. Ask almost anyone who is approaching their twilight years just how much of a waste of time that is... Don't waste your best years trying to live up to the world's standard of success, just find whatever it is that you love to do and go out and do it. Of course you need money to live, but unless you are literally a slave, your job will not define your potential.
A job should not define who a person is or what they are capable of. The only true measure of success is whether you are doing something with your life that makes you feel happy and fulfilled. Obviously you need to worry about the more fundamental needs like simple survival first, but unless you are *literally* a slave, there is nothing stopping you from doing other things as well. Regardless of how much or how little money you make, you will have always have the best chance of being happy with your own life when you do what you love... and that's where the true measure of success is.
What I'm getting at is that you're dismissing how much luck you had in not being stuck some place like the Gaza Strip or suffering from a serious neurological condition.
To the best of my knowledge, essential tremors are considered a probable precursor to Parkinson's, and as such is technically a neurological condition. Don't assume.
It's easy to be high and mighty and say things like you're saying, but not everybody has that sort of luck and a lot of this is luck. Not everybody can be a success and some people start out closer than other people do.
What I am talking about has absolutely nothing to do with "success", it is about doing what you find fulfilling in life. Regardless of how privileged anyone starts out in this world, we all end up as dust in the end.... I am saying that you should focus your efforts on making the most out of the limited time that you have here, and do what makes YOU happy... you need money to live, obviously, but a person's job should not define who they are or what their passions are unless they happen to be fortunate enough to already be getting paid for whatever it that they have a passion to do.
And surprisingly, even that's not as uncommon as you might think. There is no reason to ever let go of that dream... regardless of how long it takes you. However unlikely you may believe that achieving such goals might be, it is a *certainty* that they will remain out of reach if you don't try.
Or, you know, doing what you love will mean that you get to spend as many hours of your time on this earth as time and circumstances permit doing something that you actually enjoy.
If you like writing, then write. You'll probably get rejected... in fact, you'll probably get rejected a *LOT*. But then, if you think about it.... you would still doing what you love, which is writing... and whether or not somebody else publishes your works to your monetary benefit is wholly irrelevant to that purpose. Obviously while things aren't working out as a writing career you have to do a job that isn't your ideal to make ends meet... but your job should not define you, and it should not prevent you from still spending time and effort doing what you love.
Perhaps you didn't notice that I said that most people have to settle for doing jobs that they don't necessarily like to do to get by.... I certainly did.... for most of my life in fact. But a job should not define you unless you happen to already love doing that job.
Again, who says I was born in a decent place? Who says that one must necessarily only have good fortune. or enjoy early success to live a happy life?
And if you have to draw on exceptional circumstances like brain injuries or mental illness to make your point, I'm not sure how much you really believe what you are saying, yourself.
As I said above, you get only one shot at this life, and then you are gone. Why not try to make it best one you can? I'm sorry for you if you don't believe that your life is worth trying to be happy, but who are you to project that attitude on most people?
Why, somehow, do you think I didn't struggle, or that I enjoyed a life that was particularly well off?
When things go wrong, and you fall short of your goals, and unfortunately, we all experience failures then you take whatever it is that you *DO* have, and you do what you can with it.. That should *NEVER* mean giving up on what you love to do... it might mean you can't do it for a living right now... but that doesn't mean it's permanent, and one should not ever settle on striving for less than what they love, because while following your passion doesn't make you necessarily rich, it at has the best chance of not leaving you with any real regrets in your life. And being happy with how you've lived your life, especially as you grow older and reflect upon it, is something that no amount of money or material success can ever hope to compensate for.
My kids are all grown up now, and some are married with little ones of their own now... but this is the advice that I gave them. There's no promise of great wealth in it, certainly I am not overwhelmingly successful by most wordly standards, and unless you are very very very lucky, you will have to settle sometimes or maybe even a lot of times on doing jobs that you dislike just to survive, but you get only one chance at living... and by gosh, if you don't do everything in your own ability to try and make that life as happy as you possibly can, then there will always be some part of you that resents the compromises that you made to get to wherever it is that you are.
Do what you love.
Period.
*EVERYTHING* else is secondary to that. I won't sugar-coat it... society doesn't owe you any fortune or any success, but you *do* owe yourself the chance to be as happy as you can... and you will have nobody to blame but yourself if you don't do everything you can to achieve that end.
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D'oh.... stupid freudian typo... didn't notice until after I had submitted.
What I meant in my first sentence above was this:
There are several well known proofs that division by 0 is undefined, such as treating division as multiplication by the multiplicative inverse, much as addition as adding the additive inverse, which I mentioned above. If you are partial to calculus (actually, this is precalc-level stuff), another relatively straightforward proof is to consider the limit of division by some number x as x approaches 0 from the positive side vs division by x as x approaches 0 from the negative side. The two limits both have a magnitude of infinity, but are of opposite sign. This means that there is a discontinuity in division by 0, and because there are no mitigating factors in a division operation that suggests that only one of the limits would actually be correct at that value, mathematically it is undefined. For the case of 0/0, consider that the limit of 0/x as x approaches 0 is quite well defined, being 0, and the limit of x/x as x approaches 0 is also well defined, being 1. However, again there are no mitigating factors that suggest only one of these limits would be correct, so this means that you still have a discontinuity at 0, and in absence of any particular reason to choose one limit over the other at 0, that means that expression is undefined as well.
So no.... I am not factually wrong about this.
No... the post that RackinFrackin replied to was factually wrong. A number divided by 0 is *NOT* defined as either plus or minus infinity. The definition of division is such that any division by a number is equivalent to multiplying by that number's multiplicative inverse, but 0 does not have such an inverse, so dividing by 0 is like trying to multiply by a number that doesn't even exist.
In other words, it's undefined. Nothing more, and nothing less.
Division doesn't really exist in the sense of a mathematical operatoin. Division is best thought of as a convenient shorthand for multiplication by the multiplicative inverse of a number. The multiplicative inverse of a number is well defined to be such that a number multiplied by its multiplicative inverse equals the multiplicative identity value, which is 1. There is no number that can be multiplied by zero to get a value of 1, however, so "dividing by zero" is like trying to multiply by a number that doesn't exist in the first place.
For definitions of "well-defined" that selectively ignore the definitions that mathematicians use, perhaps.
For myself, in particular, I wonder how long it will take v8 to support it.
Bill C51 is particularly troubling... it has already been passed into law and as such may prove very difficult to get rid of by any later prime minister that disagrees with it without a majority government.
The most particularly troubling aspect of C51 is that it empowers CSIS to break almost *ANY* law... short of inflicting enduring physical bodily harm on someone, or acts of sexual violation... in the course of disrupting anything that they believe, rightly or wrongly, to be a terrorist threat, including violating even civil and constitutional rights. That means they can imprison people because of their race, or simply because of what that person believes, for example, even if that person has done absolutely nothing wrong. if CSIS has any reason at all to suspect that such factors link them to committing any act that corresponds with a terrorist threat, a phrase that by itself is so loosely defined (in fact, it isn't even defined in this law... in fact, it appears almost intentional to have left it undefined so that CSIS could apply the term as they saw fit), that even picketing or almost any other form of entirely peaceful assembly that might happens to disrupt some activity that the government is wanting to push forward could qualify.
It's interesting to consider, however, that because CSIS also outlaws the the distribution of terrorist propoganda, if, for example, Westboro Baptist Church were Canadian, then by Bill-C51, the government would have to ban the Christian bible, since WBC uses that text to justify many of their insane acts, and the bill explicitly outlaws the dissemination of literature that encourages acts of terrorism.
... tying something you physically possess to identification, but it should never be used standalone. A password, pass-phrase, or even a pin should still be required, because anything else can always potentially be taken from you, or worse yet... compromised. The additional factor of having some physical device that can further confirm your identity gives an added layer of security over the password by itself that can still be beneficial, but it should never be trusted to the exclusion of a password.
Of so, they are independent contractors, to the best of my understanding.
If one is an employee, then they are subject to things like minimum wage laws, which requires at least some participation by the employer to affect what hours the employee works.
Actually, he patterned the file system after Minux, not Multix. He did not use any Minux code.
While what Linux would ultimately become was certainly not built entirely from scratch, particularly after the GNU tools started getting bundled with it, Linus most definitely *DID* start from scratch.
So given a choice between both the poor and the rich being taxed or the poor simply starving to death because what they could allegedly otherwise afford to feed themselves isn't available, you'd run with the latter?
Interesting.
Enlighten me then.... why has the same logic for banning products not been applied to cigarettes and related tobacco products?
Actually, yes he did... unless you have a definition of "from scratch" that is so absurdly overbroad to the point that the expression no longer carries any meaning.
Incorrect.... you can make it yourself from other products.
True... but in the long term, the net effect is still positive... you cut down on the number of people that consume the product. Only a moderate level of enforcement, that is where it happens to be detected through procedures that are already occurring, would be required to be effective in the long run.
But the point you make prompts the question: why is the FDA banning transfat and not banning cigarettes, which have a much longer track record of causing health problems?
This way, people have a choice.
If the tax is sufficiently high, then in practice, the people who will consume it the most will tend to be richer... and can generally more readily afford to pay for any of the extra health care they may need because of a poor diet.
As a side effect, it also offers a revenue stream.
Actually, if an employee is smart about things, they will keep a really solid paper trail of what has been happening that leads up to their actual resignation. There are limits to what an employer is permitted to do that does not qualify as what is termed "constructive dismissal", and an employee who is on the ball when things start to heat up at work can still qualify for unemployment benefits even if they quit, if they can clearly document the circumstances behind it, and it can be shown that the employer was evidently deliberately doing things to try and get the employee to quit. It requires, however, that every incident needs to be meticulously logged, with dates, times, names of people that were involved, and where the incident occurred (on the phone, on the job site, or what have you). If you are good enough at keeping records, it shouldn't even require any real collaboration by the employer, because you will have enough documentation that the incidents can be verified independently (if one of the incidents involved changed your shift on you without giving you enough notice, for instance, you can show the logs on your cell phone records indicating exactly when they had called, leaving you inadequate time, as just one example).
Only if you measure reward by monetary gain. A pretty shallow standard, actually... you need money to live, obviously, but beyond that, your time is much more wisely invested in doing what you love. If you love philospy study philosophy.... for what it's worth, there are applications of philosophy to computer science anyways.
But trying to maximize monetary profit is a senseless goal. Ask almost anyone who is approaching their twilight years just how much of a waste of time that is... Don't waste your best years trying to live up to the world's standard of success, just find whatever it is that you love to do and go out and do it. Of course you need money to live, but unless you are literally a slave, your job will not define your potential.
A job should not define who a person is or what they are capable of. The only true measure of success is whether you are doing something with your life that makes you feel happy and fulfilled. Obviously you need to worry about the more fundamental needs like simple survival first, but unless you are *literally* a slave, there is nothing stopping you from doing other things as well. Regardless of how much or how little money you make, you will have always have the best chance of being happy with your own life when you do what you love... and that's where the true measure of success is.
To the best of my knowledge, essential tremors are considered a probable precursor to Parkinson's, and as such is technically a neurological condition. Don't assume.
What I am talking about has absolutely nothing to do with "success", it is about doing what you find fulfilling in life. Regardless of how privileged anyone starts out in this world, we all end up as dust in the end.... I am saying that you should focus your efforts on making the most out of the limited time that you have here, and do what makes YOU happy... you need money to live, obviously, but a person's job should not define who they are or what their passions are unless they happen to be fortunate enough to already be getting paid for whatever it that they have a passion to do.
And surprisingly, even that's not as uncommon as you might think. There is no reason to ever let go of that dream... regardless of how long it takes you. However unlikely you may believe that achieving such goals might be, it is a *certainty* that they will remain out of reach if you don't try.
Or, you know, doing what you love will mean that you get to spend as many hours of your time on this earth as time and circumstances permit doing something that you actually enjoy.
If you like writing, then write. You'll probably get rejected... in fact, you'll probably get rejected a *LOT*. But then, if you think about it.... you would still doing what you love, which is writing... and whether or not somebody else publishes your works to your monetary benefit is wholly irrelevant to that purpose. Obviously while things aren't working out as a writing career you have to do a job that isn't your ideal to make ends meet... but your job should not define you, and it should not prevent you from still spending time and effort doing what you love.
Perhaps you didn't notice that I said that most people have to settle for doing jobs that they don't necessarily like to do to get by.... I certainly did.... for most of my life in fact. But a job should not define you unless you happen to already love doing that job.
Again, who says I was born in a decent place? Who says that one must necessarily only have good fortune. or enjoy early success to live a happy life?
And if you have to draw on exceptional circumstances like brain injuries or mental illness to make your point, I'm not sure how much you really believe what you are saying, yourself.
As I said above, you get only one shot at this life, and then you are gone. Why not try to make it best one you can? I'm sorry for you if you don't believe that your life is worth trying to be happy, but who are you to project that attitude on most people?
Why, somehow, do you think I didn't struggle, or that I enjoyed a life that was particularly well off?
When things go wrong, and you fall short of your goals, and unfortunately, we all experience failures then you take whatever it is that you *DO* have, and you do what you can with it.. That should *NEVER* mean giving up on what you love to do... it might mean you can't do it for a living right now... but that doesn't mean it's permanent, and one should not ever settle on striving for less than what they love, because while following your passion doesn't make you necessarily rich, it at has the best chance of not leaving you with any real regrets in your life. And being happy with how you've lived your life, especially as you grow older and reflect upon it, is something that no amount of money or material success can ever hope to compensate for.
My kids are all grown up now, and some are married with little ones of their own now... but this is the advice that I gave them. There's no promise of great wealth in it, certainly I am not overwhelmingly successful by most wordly standards, and unless you are very very very lucky, you will have to settle sometimes or maybe even a lot of times on doing jobs that you dislike just to survive, but you get only one chance at living... and by gosh, if you don't do everything in your own ability to try and make that life as happy as you possibly can, then there will always be some part of you that resents the compromises that you made to get to wherever it is that you are.
Do what you love.
Period.
*EVERYTHING* else is secondary to that. I won't sugar-coat it... society doesn't owe you any fortune or any success, but you *do* owe yourself the chance to be as happy as you can... and you will have nobody to blame but yourself if you don't do everything you can to achieve that end.