Why does AC make you nervous? It's used in most major areas of mathematics. "Countable union of countable sets is countable" needs choice. "Every vector space has a basis" needs choice. AC is coool.
It's not quite that simple. Your function isn't well-defined. Furthermore, I believe you would need the Axiom of Choice just to show that such functions exist.
Nope. You don't want to do it that way. Since there is an error in your computation of a, your quotient poly has different roots than the original poly. Furthermore, the roots of polys are very sensitive to changes in the coefficients.
That's nothing man. When I was 6, I decided to perform my first scientific experiment and jam a fork into an electrical socket! I turned it loose right when it went in and received no shock. But, the circuit breaker tripped, and the faceplate was blackened. Immediately thereafter I heard my father's voice booming "Boy! Whatcha doing in there!?!"
we need to get our sense of direction. Where are we headed as a species? Looming on the horizon are the consequences of overpopulation, pollution, deforestation, and a dwindling supply of energy (read fossil fuels). When I mention these things in conversation, most people either seem to be unaware that these problems exist, or have faith that somehow God or human ingenuity will take care of everything.
Do these subjects get serious attention in school? Or are we too distracted by shopping?
I haven't tried OO yet. I may check out their spreadsheet. As for preparing documents, I'm sold on LsTeX, and really don't feel compelled to investigate alternatives. It does EXACTLY what I want it to do. Thanks.
Guess again. You are NEVER done. Otherwise there would be no need to download patches, virus updates, etc. If you never even connect to a network of any kind, and keep your computer locked in a vault that you alone have access to, you are still not 100% secure --- viruses can ride on retail software.
They never seem to run out of energy and they never seem to run out of recruits.
And, most importantly, they never run out of money. Once liability insurance was mandated, they have a steady income stream. They funnel part of this into politicians pockets, to make more laws that will make them more money, etc., etc., ad infinitum.
I agree. I teach mathematics, and have to prepare exams with equations, etc. Word does a crappy job of formatting equations. Whenever I use word, I feel like I'm sitting at a typewriter, with someone standing beside me who waves a dictionary in my face, randomly strikes keys on the typewriter, and yanks the paper out before I'm finished --- the word-processor is fighting me every step of the way. Finally, I gave up, and decided to write the exams by hand: because it was quicker to do it that way. That is, until I learned LaTeX.
I've had similar experiences with Excel. I used MS Works at home to enter my students grades. I saved it as a few different flavors of Excel, none of which would display on the most recent version of Excel on the computers at school. Frustrating.
What's sad is that at my college, the computers are brand new and loaded with Word, Excel, Powerpoint, you name it --- Microsoft. And yet, the only use they are to me is to print out PDF's using the freely available Acrobat Reader. They can't even display a postscript file.
I no longer use MS products for work --- Not because I hate Bill Gates, not because MS is a convicted monopolist, not because I am a Linux zealot. I don't use them because they cannot do what I need them to do.
You need to expand your horizons. I've used my Swiss Army knife for such diversified tasks as tuning my carburetor and slicing a wedding cake. You never know when you may need one of these little James Bond tools.
As much as we all love to hate Microsoft, I have to admit, they do make a good mouse
Hmmphh! I bought one of their plain vanilla mice a couple years ago. The piece of shit broke within 2 months -- as in the arrow jumping across the screen and otherwise not correctly responding. I bought a Logitech optical and have been happy ever since.
Men and women are NOT equal. Under any reasonable definition of equality of two things, the things should be completely interchangeable. As the grandparent pointed out, try to substitute man for woman in the phrase "the woman got pregnant" or he/his for she/her in "she had her menstrual cycle" to see the non-equality of men and women.
As in mathematics, you should say with respect to what that two things are to be considered "equivalent". For example, with respect to treatment under the law, women and men are (or should be) equivalent or equal.
As far as the insurance thing goes, insurance companies dont owe you shit.
Of course they don't. They have the benefit of twisting the government (a government that I subsidize with my tax dollars) around its little finger, and forcing me to cough up more of my hard-earned pay to support their little extortion scheme vis-a-vis mandatory liability auto insurance.
Man, I wish I could force people by law to financially support my line of work.
You know what's better than a grammar checker? A dictionary. When you go out of your way to actually look up the word, you might just end up remembering how to spell it!! Before long, you won't need to check your spelling.
Why is it that (at least in the U.S.) if you mention that not everyone is capable of playing basketball like Larry Bird, it is implicitly understood that you are correct; but, mention that not everyone is capable of learning how to solve differential equations, and you are labeled an "elitist prick"? Or better yet, a "racist" as the grandparent implied with the bit about me being a white kid. Bit of a double standard, isn't it? Do you honestly believe that EVERYONE is capable of not only mastering one academic discipline, but demonstrating a working knowledge of several others? That is a fantasy.
Tell you what: let's apply the current type of thinking about education in reverse. How about we send everyone to football training. Now, no matter how poor a player little Johnnie/Janie is, we're going to say they are a professional football player anyway. What happens next?
And getting good grades ...
on
Cheating Made Easy
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· Score: 3, Insightful
becomes the primary goal when "no child gets left behind." Now I know it is non-politically correct to say this, but not everyone is college material. Back in the day, college was intended for the cream of the intellectual crop. Now it's been watered down to job training and high school remediation. Everyone wants a college degree. Is it mere happenstance that the rise of grade inflation on the part of the teachers and cheating on the part of the students coincided with swarms of people enrolling in college?
Wow! I didn't know that --- which is why I asked. To have 613 digits of precision (as default behavior anyway) seems like a design flaw to me. I can't think of any application that requires that kind of precision except crypto and modeling proteins or something --- neither of which I can see being routinely done on a calculator.
How so? It should not be a greater problem than multiplying two 6 digit numbers together --- after all, these calculators don't display full precision on numbers like 50!, do they?
I don't have a TI or a HP-49g+. Are you saying that these calculators are actually displaying 65-digit numbers like 50! ? Or, that they are internally representing the calculations using multi-precision arithmetic?
I had a 48SX for 12 years until the button started to fail --- sometimes taking 3 or 4 presses to work. I'm a math/science teacher, and I used the 48 in class quite a bit. I suspect that some chalk dust got inside and gummed up the keys. I decided to dissasemble it for cleaning. To quote Paul Reubens from Mystery Men --- "Big Mistake!!!" I never could put the keyboard overlay completely back into place.
Well, the problem got worse, until it was barely useable. Fortunately I grabbed a replacement on ebay for about $30.
I haven't RTFA, but I wonder if they understand the notion of a 1-1 correspondence, or if they would be willing to trade 5-many apples for 3-many oranges.
Slashdot Mirror
Why does AC make you nervous? It's used in most major areas of mathematics. "Countable union of countable sets is countable" needs choice. "Every vector space has a basis" needs choice. AC is coool.
Aha! That sounds right to me.
It's not quite that simple. Your function isn't well-defined. Furthermore, I believe you would need the Axiom of Choice just to show that such functions exist.
Nope. You don't want to do it that way. Since there is an error in your computation of a, your quotient poly has different roots than the original poly. Furthermore, the roots of polys are very sensitive to changes in the coefficients.
That's nothing man. When I was 6, I decided to perform my first scientific experiment and jam a fork into an electrical socket! I turned it loose right when it went in and received no shock. But, the circuit breaker tripped, and the faceplate was blackened. Immediately thereafter I heard my father's voice booming "Boy! Whatcha doing in there!?!"
Do to massive copyright infringement, whenever someone prints out copyrighted materials they will receive an electric shock!!
we need to get our sense of direction. Where are we headed as a species? Looming on the horizon are the consequences of overpopulation, pollution, deforestation, and a dwindling supply of energy (read fossil fuels). When I mention these things in conversation, most people either seem to be unaware that these problems exist, or have faith that somehow God or human ingenuity will take care of everything.
Do these subjects get serious attention in school? Or are we too distracted by shopping?
I haven't tried OO yet. I may check out their spreadsheet. As for preparing documents, I'm sold on LsTeX, and really don't feel compelled to investigate alternatives. It does EXACTLY what I want it to do. Thanks.
That's it. You're done.
Guess again. You are NEVER done. Otherwise there would be no need to download patches, virus updates, etc. If you never even connect to a network of any kind, and keep your computer locked in a vault that you alone have access to, you are still not 100% secure --- viruses can ride on retail software.
They never seem to run out of energy and they never seem to run out of recruits.
And, most importantly, they never run out of money. Once liability insurance was mandated, they have a steady income stream. They funnel part of this into politicians pockets, to make more laws that will make them more money, etc., etc., ad infinitum.
I agree. I teach mathematics, and have to prepare exams with equations, etc. Word does a crappy job of formatting equations. Whenever I use word, I feel like I'm sitting at a typewriter, with someone standing beside me who waves a dictionary in my face, randomly strikes keys on the typewriter, and yanks the paper out before I'm finished --- the word-processor is fighting me every step of the way. Finally, I gave up, and decided to write the exams by hand: because it was quicker to do it that way. That is, until I learned LaTeX.
I've had similar experiences with Excel. I used MS Works at home to enter my students grades. I saved it as a few different flavors of Excel, none of which would display on the most recent version of Excel on the computers at school. Frustrating.
What's sad is that at my college, the computers are brand new and loaded with Word, Excel, Powerpoint, you name it --- Microsoft. And yet, the only use they are to me is to print out PDF's using the freely available Acrobat Reader. They can't even display a postscript file.
I no longer use MS products for work --- Not because I hate Bill Gates, not because MS is a convicted monopolist, not because I am a Linux zealot. I don't use them because they cannot do what I need them to do.
You need to expand your horizons. I've used my Swiss Army knife for such diversified tasks as tuning my carburetor and slicing a wedding cake. You never know when you may need one of these little James Bond tools.
I did clean it. It stayed broken.
As much as we all love to hate Microsoft, I have to admit, they do make a good mouse
Hmmphh! I bought one of their plain vanilla mice a couple years ago. The piece of shit broke within 2 months -- as in the arrow jumping across the screen and otherwise not correctly responding. I bought a Logitech optical and have been happy ever since.
Men and women are NOT equal. Under any reasonable definition of equality of two things, the things should be completely interchangeable. As the grandparent pointed out, try to substitute man for woman in the phrase "the woman got pregnant" or he/his for she/her in "she had her menstrual cycle" to see the non-equality of men and women.
As in mathematics, you should say with respect to what that two things are to be considered "equivalent". For example, with respect to treatment under the law, women and men are (or should be) equivalent or equal.
As far as the insurance thing goes, insurance companies dont owe you shit.
Of course they don't. They have the benefit of twisting the government (a government that I subsidize with my tax dollars) around its little finger, and forcing me to cough up more of my hard-earned pay to support their little extortion scheme vis-a-vis mandatory liability auto insurance.
Man, I wish I could force people by law to financially support my line of work.
You know what's better than a grammar checker? A dictionary. When you go out of your way to actually look up the word, you might just end up remembering how to spell it!! Before long, you won't need to check your spelling.
Why is it that (at least in the U.S.) if you mention that not everyone is capable of playing basketball like Larry Bird, it is implicitly understood that you are correct; but, mention that not everyone is capable of learning how to solve differential equations, and you are labeled an "elitist prick"? Or better yet, a "racist" as the grandparent implied with the bit about me being a white kid. Bit of a double standard, isn't it? Do you honestly believe that EVERYONE is capable of not only mastering one academic discipline, but demonstrating a working knowledge of several others? That is a fantasy.
Tell you what: let's apply the current type of thinking about education in reverse. How about we send everyone to football training. Now, no matter how poor a player little Johnnie/Janie is, we're going to say they are a professional football player anyway. What happens next?
becomes the primary goal when "no child gets left behind." Now I know it is non-politically correct to say this, but not everyone is college material. Back in the day, college was intended for the cream of the intellectual crop. Now it's been watered down to job training and high school remediation. Everyone wants a college degree. Is it mere happenstance that the rise of grade inflation on the part of the teachers and cheating on the part of the students coincided with swarms of people enrolling in college?
Wow! I didn't know that --- which is why I asked. To have 613 digits of precision (as default behavior anyway) seems like a design flaw to me. I can't think of any application that requires that kind of precision except crypto and modeling proteins or something --- neither of which I can see being routinely done on a calculator.
How so? It should not be a greater problem than multiplying two 6 digit numbers together --- after all, these calculators don't display full precision on numbers like 50!, do they?
I don't have a TI or a HP-49g+. Are you saying that these calculators are actually displaying 65-digit numbers like 50! ? Or, that they are internally representing the calculations using multi-precision arithmetic?
I had a 48SX for 12 years until the button started to fail --- sometimes taking 3 or 4 presses to work. I'm a math/science teacher, and I used the 48 in class quite a bit. I suspect that some chalk dust got inside and gummed up the keys. I decided to dissasemble it for cleaning. To quote Paul Reubens from Mystery Men --- "Big Mistake!!!" I never could put the keyboard overlay completely back into place.
Well, the problem got worse, until it was barely useable. Fortunately I grabbed a replacement on ebay for about $30.
The 48 is the best calculator I've ever owned.
And even today, there are those who believe that zero is not a number. Do a Google search, and be a-mazed/mused.
I haven't RTFA, but I wonder if they understand the notion of a 1-1 correspondence, or if they would be willing to trade 5-many apples for 3-many oranges.