it's surprising how few people know that a four sector tower only covers about 250 moderately heavy users (think 3G speeds) in a ~50KM bubble. the 100 bubbles you have to cover an entire country (or in many cases many countries) hardly cover the province I live in. (on top of that they don't deploy at ~50km spacing here, our incumbent Telco here maintains a poor sixty three towers: to cover the 650,000KM^2 province. and trust me, they don't have fiber run out to 80% of them, meaning the towers get a single T1 for total bandwidth backhaul's.
where one telco covers Europe with "decent coverage/speed" for $250,000, one in north america covers one major city for the same budget. there are 160 Cities in Canada alone: that's a lot of dough.
the definition of a sine is nothing more than a ratio between the angle of a triangle and the length of the sides. in the real world, we cannot use undefinable units of measure to determine anything useful: we need to measure the degree of accuracy.
an example of this is the value of pi: how many times must you rotate a circle to allow any one point on the shape to return to the same point on a Cartesian plot? mathematically the circle must rotate [pi] times for this to happen thus sin(pi) = 0. but how do you determine when this rotation has completed? you can only do so by assuming a degree of accuracy: your point cannot be a "point" (they don't exist in the real world, as defined under the uncertainty principle) it must be an area containing the point you intended. there's no way to determine where that point is once measured the first time (under standard quantum mechanics) instead you can only estimate where it will be the second time.
in exactly that case, the point will NOT require a [pi] rotation to return to the original coordinates: as that would have to happen in 0.0 seconds, instead it will have traveled during Ts to a new location, resulting in the value being [pi +/- the degree of accuracy]
the point I'm trying to make is simply that: when you define something that can't exist (like an infinity repeating fraction) and try to perform arithmetic on it, the answers you get have no real value: they're just hypothetical values that have no place in the real world.
the 0.999...
math only exists to answer questions. there's no reason playing with the extents of the system in ways like this: as they have no real world ramifications (except that it reveals areas that the theory may be flawed)
just because the definitions are what they are, is what allows this problem to be so misunderstood. if I go back a few hundred years, I can prove without a possible doubt (on paper) that the earth is flat. one day, the definitions will change, and this "common knowledge" will be seen as false.
tl;dr: 0.999... = 1 only if you accept definitions that may or may not be accurate, and being that they cannot describe the real world at any scale: I assume them to be inaccurate.
but symbolic computations are just that: symbolic.
you cannot represent much of out mathematics in the real world, which is where computation plays so wonderfully. give me a real world example of sin(pi)=0
I can tell you for sure, that no matter how you experiment, and no matter how accurate you think the answer is, it's not true in the mathematics sense.
the value of pi that we determine is based on the idea that a perfect circle exists. as we know from nature, no arc shaped structures really exist (at the atomic level, they much more closely represent a Cartesian Plane) though with the effect of magnetism they may act significantly more LIKE circles. (though never truly are)
the problem is that we do math based on the concept of perfect objects. as we know, they don't really exist, so we must instead turn to the idea that math is simply approximations based on the degree of accuracy that you need. (after all, ~39 decimal places will give you a margin of error of less than the size of an atom of hydrogen. a pretty acceptable value for most.)
quantum mechanics will introduce you the idea, though the theory still leaves much to be discovered.
the math that we know is based on theory. that theory comes from real principals: the idea of 1/9'th comes from the idea that we can separate one object into nine equal parts.
now the trick that get's messy, is that we have yet to determine IF there is a fundamental particle. if there is: then there is no infinity. there's just a f'in HUGE number of decimal places, and absolute numbers. if there isin't (and particles just keep getting smaller and smaller) then the math we have fails to describe them.
if you take an object and divide it into nine "equal" parts, you and I both know that you have eight parts that may be about equal, and one that's slightly bigger/smaller, or we have nine equal parts that have equal numbers of (mass/volume/whatever) but they each have a finite amount of each. thus we can determine that.999... != 1, but rather 0.333+0.333+0.334 = 1
and 0.333+0.333+0.333 =.999
you can only do classical math if you know the precision of your calculation. that's a limit we have, and depending on how the universe works, it might be correct.
So 10 multiplied by (1/9) would be the same as (1/9) + (1/9) +... + (1/9) ten times. Or are you saying that we can't add either?
No, you can't. 1/9 cannot be added to 1/9. you can't add 1 to infinity, you can't multiply infinity by two.
you can add an approximation of 1/9 to an approximation of 1/9, but like I already mentioned earlier: it's like people claiming to use the value of pi in math: you can't! you can only use a definable approximation of pi.
like any sane person, people know that pi != 3.14, just like pi != 3.141592
pi IS however roughly equal to 3.14, and slightly more equal to 3.141592 but never does it equal it.
exactly! [infinity] minus [infinity] does not equal zero. you can't subtract everything from something, you'd have nothing left to make a measure of.
this makes more sense when you think of division: [infinity] / [anything, EVEN infinity] != 1
as you cannot divide an infinite number of anything into any quantity. as much as people like to think of being able to perform math on infinity, you can't perform classical mathematics on it.
I'm sorry, but as much as anybody want's to multiply an infinity repeating fraction by a limited decimal, you can't. it would be the equivalent to adding an int to a float. as much as you try to claim the precision of your float, you can only perform basic operations up to your decimal limit.
thus: if a=(1/9)
10a can't happen: you need to multiply by a float. and saying 10.0 is a float, means that.9 = 10(.1) which is false.
and the children that struggle and are unable to progress in the education system because of how poorly it's forced on them to learn things that will never be applicable to their lives?
everybody's different. I've been saying for YEARS that the education system needs a MAJOR overhaul. maybe some day soon the people being voted in from today's generation MIGHT start listening!
"Oh, HERE they are! silly buggers, I though you ran away!"
seriously though, stuff like this DOES happen. the UK Government just shut down what, hundreds of websites that they didn't even know they had been paying for?
I expect people (who do their work on computers 6-8 hours a day) to be able to read an error message and fix their own icon arrangement without me babysitting them.
I'm sorry to have to say this, but uneducated people are not idiots.
I expect one of two things: you work with people who were raised without computers, and as such have never had a chance to learn how do do some of these basic tasks. (please, try sometime going to a library and reading an "intro to computers" book and look at the shit they try and teach people.)
OR, you work with younger workers, who are used to having somebody to call whenever something unexpected happens. these people frighten me a little, as they seem to have NO intelligence of any sort in their heads: except that they do. uneducated people just need to know how to do something, and know that it's their responsibility to try to fix it.
people these days LOVE to not have to be responsible. I know people that have TURNED DOWN JOBS!! because the place they applied for didn't have an IT person on staff (they instead contracted major work out) to click yes to check boxes and to do the windows updates (etc) on the PC's.
I don't know where you live, but in local computer stores here in Manitoba Canada, that happens all the time.
seriously. people over the age of 55 bring in computers to shops all over, with a message "your antivirus application would like to update, click ok to start this process". and are happy to pay $30-$50 or $80/hour to have somebody do it for them.
You’ll have to turn off the AV and executable file filter to download it, of course...
turn off... the... what..?
am I the only person in the world these days that doesn't run AV on personal PC's? jebus, I wouldn't even know what to buy anymore.
the itinerary for ANY level of education all the way from grade four to a doctorate course in a university for computer sciences:
1) Computer Sciences.
1.a) Microsoft Windows. (if funding was provided by MS.)
1.b) Unix security
2) Programming
3) Keyboarding
and that's honestly about it. on a sheet of paper, with the school's letterhead at the top. if you're LUCKY, they might have what has been taught there for the last several years.
teachers today have almost complete control over what they teach, in most districts.
glad to know I'm not the only one! my task bar also made it to the far left of a dual 1900X1200 setup. (though it's a pain to see it all the way down there, I have to turn my head to see it!)
Slashdot Mirror
Exactly.
it's surprising how few people know that a four sector tower only covers about 250 moderately heavy users (think 3G speeds) in a ~50KM bubble. the 100 bubbles you have to cover an entire country (or in many cases many countries) hardly cover the province I live in. (on top of that they don't deploy at ~50km spacing here, our incumbent Telco here maintains a poor sixty three towers: to cover the 650,000KM^2 province. and trust me, they don't have fiber run out to 80% of them, meaning the towers get a single T1 for total bandwidth backhaul's.
where one telco covers Europe with "decent coverage/speed" for $250,000, one in north america covers one major city for the same budget. there are 160 Cities in Canada alone: that's a lot of dough.
very well stated. I'd mod you up if I could.
the definition of a sine is nothing more than a ratio between the angle of a triangle and the length of the sides. in the real world, we cannot use undefinable units of measure to determine anything useful: we need to measure the degree of accuracy.
an example of this is the value of pi: how many times must you rotate a circle to allow any one point on the shape to return to the same point on a Cartesian plot? mathematically the circle must rotate [pi] times for this to happen thus sin(pi) = 0. but how do you determine when this rotation has completed? you can only do so by assuming a degree of accuracy: your point cannot be a "point" (they don't exist in the real world, as defined under the uncertainty principle) it must be an area containing the point you intended. there's no way to determine where that point is once measured the first time (under standard quantum mechanics) instead you can only estimate where it will be the second time.
in exactly that case, the point will NOT require a [pi] rotation to return to the original coordinates: as that would have to happen in 0.0 seconds, instead it will have traveled during Ts to a new location, resulting in the value being [pi +/- the degree of accuracy]
the point I'm trying to make is simply that: when you define something that can't exist (like an infinity repeating fraction) and try to perform arithmetic on it, the answers you get have no real value: they're just hypothetical values that have no place in the real world.
the 0.999...
math only exists to answer questions. there's no reason playing with the extents of the system in ways like this: as they have no real world ramifications (except that it reveals areas that the theory may be flawed)
just because the definitions are what they are, is what allows this problem to be so misunderstood. if I go back a few hundred years, I can prove without a possible doubt (on paper) that the earth is flat. one day, the definitions will change, and this "common knowledge" will be seen as false.
tl;dr: 0.999... = 1 only if you accept definitions that may or may not be accurate, and being that they cannot describe the real world at any scale: I assume them to be inaccurate.
but symbolic computations are just that: symbolic.
you cannot represent much of out mathematics in the real world, which is where computation plays so wonderfully. give me a real world example of sin(pi)=0
I can tell you for sure, that no matter how you experiment, and no matter how accurate you think the answer is, it's not true in the mathematics sense.
the value of pi that we determine is based on the idea that a perfect circle exists. as we know from nature, no arc shaped structures really exist (at the atomic level, they much more closely represent a Cartesian Plane) though with the effect of magnetism they may act significantly more LIKE circles. (though never truly are)
the problem is that we do math based on the concept of perfect objects. as we know, they don't really exist, so we must instead turn to the idea that math is simply approximations based on the degree of accuracy that you need. (after all, ~39 decimal places will give you a margin of error of less than the size of an atom of hydrogen. a pretty acceptable value for most.)
quantum mechanics will introduce you the idea, though the theory still leaves much to be discovered.
I'm sorry, you're right. for some reason I had mixed up those two definitions in my head.
the math that we know is based on theory. that theory comes from real principals: the idea of 1/9'th comes from the idea that we can separate one object into nine equal parts.
.999... != 1, but rather 0.333+0.333+0.334 = 1
and 0.333+0.333+0.333 = .999
now the trick that get's messy, is that we have yet to determine IF there is a fundamental particle. if there is: then there is no infinity. there's just a f'in HUGE number of decimal places, and absolute numbers. if there isin't (and particles just keep getting smaller and smaller) then the math we have fails to describe them.
if you take an object and divide it into nine "equal" parts, you and I both know that you have eight parts that may be about equal, and one that's slightly bigger/smaller, or we have nine equal parts that have equal numbers of (mass/volume/whatever) but they each have a finite amount of each. thus we can determine that
you can only do classical math if you know the precision of your calculation. that's a limit we have, and depending on how the universe works, it might be correct.
So 10 multiplied by (1/9) would be the same as (1/9) + (1/9) + ... + (1/9) ten times. Or are you saying that we can't add either?
No, you can't. 1/9 cannot be added to 1/9. you can't add 1 to infinity, you can't multiply infinity by two.
you can add an approximation of 1/9 to an approximation of 1/9, but like I already mentioned earlier: it's like people claiming to use the value of pi in math: you can't! you can only use a definable approximation of pi.
like any sane person, people know that pi != 3.14, just like pi != 3.141592
pi IS however roughly equal to 3.14, and slightly more equal to 3.141592 but never does it equal it.
http://www.youtube.com/watch?v=X-jVAHAuiS4
how many atoms make up your body? though this number may change from time to time (well, A LOT!!) it is quantifiable with real numbers.
exactly! [infinity] minus [infinity] does not equal zero. you can't subtract everything from something, you'd have nothing left to make a measure of.
this makes more sense when you think of division: [infinity] / [anything, EVEN infinity] != 1
as you cannot divide an infinite number of anything into any quantity. as much as people like to think of being able to perform math on infinity, you can't perform classical mathematics on it.
Exactly.
i.e. Think of pi.
you have NEVER done math with pi. ever. without question.
you have only ever done math with an approximation of pi. there's a BIG(small) difference.
No, he just dismissed BAD mathematics.
.9 = 10(.1) which is false.
I'm sorry, but as much as anybody want's to multiply an infinity repeating fraction by a limited decimal, you can't. it would be the equivalent to adding an int to a float. as much as you try to claim the precision of your float, you can only perform basic operations up to your decimal limit.
thus: if a=(1/9)
10a can't happen: you need to multiply by a float. and saying 10.0 is a float, means that
and the children that struggle and are unable to progress in the education system because of how poorly it's forced on them to learn things that will never be applicable to their lives?
everybody's different. I've been saying for YEARS that the education system needs a MAJOR overhaul. maybe some day soon the people being voted in from today's generation MIGHT start listening!
"Oh, HERE they are! silly buggers, I though you ran away!"
seriously though, stuff like this DOES happen. the UK Government just shut down what, hundreds of websites that they didn't even know they had been paying for?
sprawl != organised.
it's in IPv6. :P
That's kind of the trick though, nobody will talk about what happened.
what we really need is somebody to talk, we'll never know what happened otherwise!
Oh if only it were so easy. *sigh*
Oh SCHWING! nice!
I expect people (who do their work on computers 6-8 hours a day) to be able to read an error message and fix their own icon arrangement without me babysitting them.
I'm sorry to have to say this, but uneducated people are not idiots.
I expect one of two things: you work with people who were raised without computers, and as such have never had a chance to learn how do do some of these basic tasks. (please, try sometime going to a library and reading an "intro to computers" book and look at the shit they try and teach people.)
OR, you work with younger workers, who are used to having somebody to call whenever something unexpected happens. these people frighten me a little, as they seem to have NO intelligence of any sort in their heads: except that they do. uneducated people just need to know how to do something, and know that it's their responsibility to try to fix it.
people these days LOVE to not have to be responsible. I know people that have TURNED DOWN JOBS!! because the place they applied for didn't have an IT person on staff (they instead contracted major work out) to click yes to check boxes and to do the windows updates (etc) on the PC's.
I don't know where you live, but in local computer stores here in Manitoba Canada, that happens all the time.
seriously. people over the age of 55 bring in computers to shops all over, with a message "your antivirus application would like to update, click ok to start this process". and are happy to pay $30-$50 or $80/hour to have somebody do it for them.
I wonder, does anybody have a link to the EULA for a PS3?
I doubt that the license is transferable, and I assume that opening the box would be justification of purchase?
are they voiding warranties?
You’ll have to turn off the AV and executable file filter to download it, of course...
turn off... the... what..? am I the only person in the world these days that doesn't run AV on personal PC's? jebus, I wouldn't even know what to buy anymore.
you ever worked in the education system?
the itinerary for ANY level of education all the way from grade four to a doctorate course in a university for computer sciences:
1) Computer Sciences.
1.a) Microsoft Windows. (if funding was provided by MS.)
1.b) Unix security
2) Programming
3) Keyboarding
and that's honestly about it. on a sheet of paper, with the school's letterhead at the top. if you're LUCKY, they might have what has been taught there for the last several years.
teachers today have almost complete control over what they teach, in most districts.
glad to know I'm not the only one! my task bar also made it to the far left of a dual 1900X1200 setup. (though it's a pain to see it all the way down there, I have to turn my head to see it!)
not to sound like a jerk here, but what you're saying is you have 1200X1900 display. :P