Slashdot Mirror

Not even if it went around the world across the Atlantic ocean, Europe, Asian, and the Pacific ocean rather than directly unless you made a trip out of the way (for example, from Europe to northern African along the way).

Current satellite Internet uses geosynchronous orbits of 22,000 miles away. The equatorial circumference of the earth is about 24,900 miles.

The circumference at the Chicago and New York latitudes of 41.9 and 40.7 respectively is less. The radius of the earth is about 3,959 miles.
The circumference at a latitude of 41.3 is approximately:
=2*pi*r
= 18,687 mi
Or you can also do:
(equatorial circumference) * cos (latitude in radians)
24,900 miles * cos((41.3/180)*pi)
= 18,706 mile
Which is slightly different because the earth isn't exactly a circle.

https://en.wikipedia.org/wiki/...
http://mathforum.org/library/d...

> why should that be NaN? 1/0 is Infinity, not NaN.

Incorrect. You need to go back to school and review what divide by zero actually means.

a/b = c
a = b*c

However when a != 0, and b =0,

a/0 = c

There is NO value of c that produces a.

a = 0*c (impossible)

Furthermore, mathematicians define division by zero as undefined because x/0 has TWO simultaneous values: +inf and -inf, depending on which side you approach x from: the negative side of zero, or the positive side of zero. The mathematical set of Reals is NOT closed under division by zero -- it produces a singularity.

0/0 is "indeterminate" which naturally maps into NaN.

console.log( 0/0 );
NaN
console.log( isNaN(0/0) );
true

All is good and fine so far.

However Javascript uses the broken IEEE 754 definition of x/0 = Infinity. This is is retarded because is broken math

Proof:

1/0 = +inf (assume retarded definition of divide by zero is valid)
0*(1/0) = 0*inf
(0/0)*1 = 0
undefined *1 = 0
NaN = 0
WTF

Note: NaN is NOT equal to ANY value, including itself.

console.log( NaN === NaN );
false
console.log( NaN == NaN );
false

> Is there some standard that says that "big" signed integers should be surreptitiously changed into unsigned ones?

Your mistake is assuming Javascript has integers in the first place. Javascript does NOT have signed integers. All values are 64-bit floating point values.

4.3.20 Number value

primitive value corresponding to a double-precision 64-bit binary format IEEE 754-2008 value

and

6.1.6The Number Type

The Number type has exactly 18437736874454810627 (that is, 264-253+3) values, representing the double-precision 64-bit format IEEE 754-2008 values as specified in the IEEE Standard for Binary Floating-Point Arithmetic, ...

One of the reasons Javashit is such a crappy language because it has no uint32_t nor uint64_t. This leads to subtle over-flow bugs that are difficult or impossible to work around.

But what do you expect from a language designed in 10 days.

The fact remains, however, that defining 0/0 or 0^0 as 1 is useful in more cases than not 1. See the short explanation or the long explanation.

You have to memorize all the perfect squares and perfect cubes of single-digit numbers. After that, you can find either.

Given that I know the decimal place is arbitrary (thanks to the soroban) and that the method follows a pattern (x^(1/n) find the largest perfect nth root of n digits), I can generalize this in many ways. By memorizing 8 numbers--the perfect exponents of 2 through 9--and operating on sets of n digits, you can compute the nth root of any number. For 4, it would be 4 digits, and all perfect 4th exponents.

For anyone who hasn't put in the effort to perform mental math of third, forth, and fifth roots, it is trivial to use mental multiplication or lattice calculation (Napir's Bones) to quickly write up 0^4 = 0, 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on. With this short list, one may then inscribe upon paper the number, the 4th root operation, and then begin with 4 digits and follow the same algorithm as with the third and second roots. Thus if you really do require the exact fifth root of a number out to 17 decimal places, you can find it with a few seconds of computation and a sheet of papyrus or a stick and some sand.

The ancients did not have the PAO system or even the Mnemonic Major system for which to chunk and retain numbers. Had they, they would have likely used them for scratch pad in mental math, along with a mind palace to compose fifteen or more computation registers of six digits each. Mental math is computed rapidly by using a great number of systems which have been always known to those of any intelligence, and are frequently rediscovered by small children.

The chief mental math system in use today is the Friendly Numbers system. As a child, I would approach problems such as 13 + 22 by first adding the 3 and 2 to get 10 + 25. When given problems such as 13 + 22 + 17 + 19 + 35, I would then see 3 + 7 and 9 + 1, changing 13 to 10 and 22 to 21 in respect, and leaving 10, 21, 20, 20, 35, and thus 10 + 20 + 20 + 30 + 20 and 5 + 1, or 106.

Another historical mental math system is that of the use of the Japanese Soroban, a 4/1 abacus. The Soroban leads the way into Anzan: while the methods of the Soroban dictate how to operate the beads, the beads only represent numerical transformations. The memorization of the complement of 7 and 3 on 10 means that 25 + 37 is equivalent to 25 - 3 + 30 + 10. Thus the first step is to add 2 + 3 to gain 50, and then to add 7 + 5, and instead provide 60 and 5 - 3, which is 2. 62. It is also memorized that 3 and 2 are complements on 5, because the Soroban toggles the 5 bead and then provides the appropriate complement (rather than 5 + 0, it becomes 0 + 2); this is less obvious when dealing with straight decimal.

In short: a person calculating via Anzan--mentally, without manipulating a Soroban--would produce 50, then produce 60 and 2, calculating from left to right. In American schools, addition is by the carry system, in which it is taught by rote: 7 + 5 is the matter of counting 5 more from 7, which is why you see many people COUNT ON THEIR FINGERS WHEN THEY ADD, and you produce 2-carry-1. The same is followed for 2 + 3, plus the carried 1. This is many more operations, and the obvious friendly number systems come about as people memorize multiples of two: 7 + 5 becomes 6 + 6 which is 12; 2 + 3 + 1 becomes 3 + 3 which is 6. Anzan takes this a step further, computing each pair of digit additions by singular atomic computation rather than iterative loops and simplifying operations.

Soroban and Anzan multiplication come down to addition, through route of memorizing all products from 1x1 to 9x9 and performing the multiplication left-to-right and adding into an accumulator. One common method is strikingly similar to lattice multiplication, which tends to require n*m or 2(n*m) single-digit multiplication operations, plus 2(n*m)-1 additions. Mentally, if you recognize all mul

Maybe he should have meant the following version which seems very counter-intuitive:

Suppose you wrap a string around the Earth's equator so that it fits tightly. Now suppose you add an extra meter in the length of that string. Surely, the string won't be tight anymore. So pinch it at a point and pull it upwards as high as you can. (Now, the string goes tightly around most of the earth, and forms a triangle elsewhere with the apex being the point you pinched and pulled.)

How high this apex would be from the surface? The answer turns out to be well over a hundred meters. See Image 1

(Apart from the actual number, the surprising part is also that the bigger the initial object - earth here - the higher you can pull the string even though you add the same extra length of 1 m in each case.)

I think he converted 40 square meters to 47 square yards, which is fairly reasonable. But then he really goofed and called it 47 yards square, which is something completely different altogether -- something that is a square with 47 yards per side!

HA! I was going to say something similar, but not quite as funny. Thanks, I needed a laugh today.

It sent me off into left field thinking of the possibilities of how much tax I owe due to saving made when I bought the home that I did, rather than buying one of these places.

I think SJHillman would be blown away by "complex math". ;)

If you don't like "nearly infinite", it might be better to avoid saying things like "a billionth of a billionth of infinite", and even "infinity minus seven", without giving some sort of definition of what you're talking about. If you mean cardinals, then the values you appear to be talking about are trivially the same as the infinite cardinal you started with. If you mean ordinals, it doesn't look like there's any well-defined thing that corresponds to the phrases you're using.

Your best bet might be to read up on hyperreals, because in that system expressions like r - 7 and r * 10^-18 do actually make some non-trivial sense where r is infinite, and your intuition is correct that there's no sensible definition of a "nearly infinite" hyperreal. But until you have some understanding of the transfer principle, or at least are familiar with the basic properties of the hyperreals, you'd be well advised to avoid such expressions, especially if you're math-naziing against everyday expressions like "nearly infinite" whose intended meaning is entirely clear. Take a look at this (or at this if you're more mathematically trained).

Not trolling -- you're obviously interested in mathematics -- just pointing your enthusiasm in a useful direction :-)

On the other hand, if someone wants to question basic arithmetic, Science should stand up to it.

Want to question whether or not 1 + 1 = 2?

Look at the Peano Postulates that define natural numbers, look at the definitions for 2 and addition, and you can independently reproduce the proof that 1+1=2.

http://mathforum.org/library/drmath/view/51551.html

We've now reached the point that arithmetic is understood and accepted as true by enough people that we don't need to bother reproducing it independently. But importantly, it _can_ be.

Of course you can proove something doesn't exist. You just need to have certain assumptions about its nature first, such that you can qualify, without any doubt, that properties which satisfy that nature cannot exist. For example, an early mathematical proof that no rational exists which satisfies the criteria of being the square root of 2 is a proof of the non-existence of something. The notion that one cannot ever prove something impossible is, itself, a fallacy of generalization.

No, but they have naturally built plant-made pesticides in their DNA ( here and here ) and naturally built plant-made carcinogens ( here and here ).

And no, I don't own Monsanto stock. Monsanto is financially evil, and this is the root of the problems with GM food, but don't let health get tarred with the same brush as economics.

it's not getting into the hands of Joe Consumer, it's going to the banks to clean up their balance sheets and make them appear solvent

What the hell do you think the bank does with the money?

Bank gives loan, calculates the interest from loan to be profit. Example:
I give you a $1000 loan, 10% interest, I've made $100. The $100 came into existence from nothing; it's conjured money.

Theoretically it's conjured with a reason: the exploitation of the planet grows at a constant rate so that the increase of currency from conjured money will be equal to the increase in physical goods and services available. There is 10% more goods available in the world by the time you finish paying me the $1100.

In reality banks get greedy: they lend too much to make more profit. The exploitation of the planet doesn't grow as fast as the currency is being inflated, the money to goods equilibrium is shifted and money is worth less than the goods it represents, this is called inflation and happens at an exponentially. Roughly 5% per year means money will be worth half every 15 years. (So the half life of money is about 15 years.. or depends on what you consider inflation rate: http://mathforum.org/library/drmath/view/54650.html)
In very grim reality:
The inflation of currency from money conjured up by bank debts is infinite because it is not based on reality. The exploitation of the planet can not continue forever because the physical resources are limited, ie there is a finite limit to the exploitation of the planet's resources. If you combine these two facts, you get a runaway inflation of currency as resource exploitation reaches its limit, the whole system is barreling towards an inevitable and catastrophic collapse that few people can even fathom. Economists tend not to see this because economics books overlook the simple fact resource exploitation can not grow indefinitely and infinitely, so this never occurs to them.

online videos: algebra + calculus
http://justmathtutoring.com/
http://www.mathtutor.ac.uk/
http://www.khanacademy.org/
http://www.graderocket.tv/index.php

Uni Maths Videos
http://ocw.mit.edu/OcwWeb/Mathematics/
http://press.princeton.edu/video/banner/
http://academicearth.org/subjects/mathematics
http://freescienceonline.blogspot.com/2009/01/calculus-video-lectures-bonus-basic.html
http://www.apple.com/education/itunes-u/ (requires iTunes download)

Resources from Universities
http://www.germanna.edu/tutor/helpful_handouts.asp?menuchoice=Helpful%20Handouts (wow)
http://mathforum.org/

Free online books:
http://www.jamesbrennan.org/algebra/systems/solution_set.htm
http://cnx.org/content/m18205/latest/?collection=col10624
http://www.jirka.org/diffyqs/ (Differential eqns)
http://www.purplemath.com/
http://tutorial.math.lamar.edu/

PowerPoints
http://www.online.math.uh.edu/HoustonACT/

Tutoring services
http://www.nutshellmath.com/

Collections of Links
http://math.about.com/od/mathhelpandtutorials/Math_Help_and_Tutorials_by_Subject_and_or_Topic.htm
http://pathstoknowledge.net/

Problems
http://projecteuler.net/

Some computer Resources
http://www.graphmatica.com/
http://archives.math.utk.edu/visual.calculus/

Helpful handouts from Germanna Community College's tutoring Center. (I used to work there a few years ago; these resources are not only helpful, but free.)
Drexel's Math Forum (full disclosure: I'm a current Drexel employee and student -- but the Math Forum strikes me as pretty cool.)
Project Euler(more oriented toward programming and numerical methods, but interesting site for developing your math skills. The problems range from not-too-hard to mind-boggling.)
Purple Math

the act of multiplying requires memorizing the tables for 1-9 first, unless you multiply by repeated addition, or your final goal is to multiply like a Russian Peasant

Hint: The vast majority of people have an above-average number of legs.

Yes, but "the vast majority" is not normally the same as "average". The normal meaning of "average" is either "arithmentic mean" or "median". As you rightly point out, the average (arithmetic mean) number of legs amongst the population is slightly below two. Using the definition on this page, the median number of legs amongst the population would be 1. Any further comparison with counting legs is not useful because the number of legs that people have has a very small range of discrete numbers.

So let's look at all three definitions of "average". Firstly, let's assume that the "years out of college at which people get H1's" has a lower bound of zero.

Arithmetic mean: Since there is a significant population of people who get H1-b's some years or even decades out of college, this will obviously set the arithmentic mean to be something more than zero.
Median: People get H1-Bs up to probably 40 years out of college, so the median value would be around 20
Mode: as I mentioned earlier, it is possible that the largest population of people who get H1-bs are zero years out of college. But I don't believe this to be true and another poster cited a webpage that supported my position.

Now, if anyone would like to take my comments above and explain exactly why I am wrong, rather than just making the claim that I am wrong without any relevant and specific explanation, I welcome it. Otherwise, I will persist in my claim that the average age at which people get H1-B visas is not "fresh out of college".

One final note. The OP actually referred to the "age at which H1-bs come into the country". Since people can come into the country on a student visa and then transfer to an H1-B, some did come into the country before graduating (although most student visa are awarded for postgraduate study). This fact is, however, not relevant to the discussion, since the original point was 22 or 23 years old plus 7 years. The 7 years being the max on an H1-b (23 or 23 being an expected age for first degree graduation). Those 7 years would apply to the time of granting the H1-b, so the original poster was wrong. In other words, if the average age at which people on H1-bs leave is around 30, I contend that the average time they spent on an H1-B was probably significantly less than 7 years. More likely 3-5 years, perhaps less even.

You cannot be serious ..

"Excel 2007, like its predecessors, fails a standard set of intermediate-level accuracy tests in three areas: statistical distributions, random number generation, and estimation"

If the specificity is 95%, and 8 samples are taken, the likelihood of a false positive in two or more cases is not a quarter of a percent, but closer to about 7%. Probability is hard. Which still leaves a big unknown: what IS the specificity, anyway? was 95% a reasonable assumption?

Above all, practice (Math is a muscle). Find some problems that you think are interesting, and solve them. If something doesn't work out the right way, try it again. Try and explain the problem to someone else -- that almost always helps.

I highly recommend this book: The Square Root of Two by David Flannery. It's an excellent book which gives some real good insight into how to think about math problems, and is a pretty fun read.

http://mathforum.org/dr.math/ is a great web site for helping with homework.

Also, don't get discouraged, Math Is Hard.

Hilbert curves are special cases of a Weinerstrauss Monster, so named, because Weinerstrauss worked on curves that were continious, and diffrentiable nowhere.

Please call these curves, Weierstrass Monsters.

So, a bit of History, Weinerstrauss was looking at the curves in the 1870s, Hilbert came along around 1890, and Maldenbront with the help of computers looked at them in the 1970s.

http://mathforum.org/library/drmath/view/61209.html ( text, but excellent refrence for Math )

Nice try.

Somehow I'm not surprised to find that materials written for consumption by grade school students (and teachers) get this wrong. A prime element of an integral domain is a non-zero non-unit p such that if p divides ab, p divides either a or b (or both). The integers are an integral domain, and (-5) is a prime.

Nice try.

What, no mention of Descartes' fly?

NSF budget FY 1983 - just over $1 billion http://en.wikipedia.org/wiki/National_Science_Foun dation
NSF budget FY 1990 - just over $2 billion http://en.wikipedia.org/wiki/National_Science_Foun dation
NSF budget FY 1995 - $3.270 billion http://mathforum.org/social/articles/nsf.budget.in fo.html
NSF budget FY 2000 - $3.747 billion http://www.nsf.gov/about/budget/fy2000/overview.ht m
NSF budget FY 2005 - $5.6 billion

Those numbers are higher as time goes forward.

Deny whatever you like--decreased science funding...

I see increased science funding.

It's not exactly hard to type "NSF budget FY 1995" into Google. Anyone can do it. Even you.

Yes any number divided by itself is 1, but you forgot another rule 0 divided into any number is 0 so 0/2=0 0/42=0 and whatnot. So 0/0 would have 2 possible answers if it followed both rules 0/0=1 and 0/0=0. However going back to my HS Algebra classes there was a solution to this called 'i' for imaginary numbers, so 2/0=i and 42/0=i. Then i could be used as a number in equations just with any answer having the 'i' at the end of it. 'i' can also be negative. See http://mathforum.org/dr.math/faq/faq.imag.num.html for a bit more information on it.

Actually I forgot the proof I was going to use so here's something similar to what our teacher showed us.

A fundamental part of his explanation pivots on the following being true: 1/0 = infinity -1/0 = -infinity So, according to that, the following would hold: if 1/0 = infinity then infinity * 0 = 1

which does not work, for obvious reasons. This I told my teacher in 6th grade.

Infinite time means everything that can happen, will.

No, it doesn't. As an analogy, the decimal representation of any irrational number goes on to infinity, but that doesn't necessarily mean that every possible number combination will appear in it.

Are All Digit Strings in Pi?

Let's say you have two different brands of HDTVs. One has a profit margin of $300, while the other has a margin of $600. Furthermore, let's say you have 4 DVDs with profit margins of $2.00, $3.00, $4.00, and $0.50. How do we compare the profits of one type of item over the other?

Well, we could use averages:

1 $300 HDTV
1 $600 HDTV
-----------
$450/unit average

600 $2.00 DVDs
600 $3.00 DVDs
800 $4.00 DVDs
1000 $0.50 DVDs
---------------
$2.23/unit average

Obviously, the HDTVs win. But that's not a very good way to actually compare your business units. A much better way is weighted averages. If we weight the averages of the products against the total sales, we find that the HDTVs are only pulling in a profit of about 30 cents for every sale made while the DVDs are pulling in $1.00 for every sale made. So which one is more valuable to be selling? The big clunky HDTVs that take up shelf space but sell poorly overall, or the DVDs which make up most of the revenue and take very little shelf space?

Of course, actual business practices would state that the HDTV is a method of selling more DVDs. So the sales of the HDTVs in the same store would be justified. But it does show how naive math can get you in serious trouble.

And he is an obvious troll. I even suspect he cut and pasted it based on the line breaks throughout.

*Googling, please wait...*

Ding ding ding! We have a winner!

But I digress.

Here's the deal. Do what you love. Don't blame us for doing what we love. To think that your chosen career is somehow "better" than someone else's is pure arrogance.

It is certainly reasonable to check out clusters of cases when the pop up, but it is important to keep in mind the natural human bias toward overestimating the statistical significance of clusters. For example, when asked to write a series of random numbers, people almost always have fewer clusters than chance would predict. Another classic example is the birthday problem, where most people wildly underestimate how big a group you need before you are likely to have two people with the same birthday.

To consider the probability of a suspicious cluster arising by chance, you can't just figure the likelihood of a cluster arising in that particular building--you have to think in terms of the probability of a cluster randomly arising in some building that is in the vicinity of something that might plausibly be blamed.

here
doh!!
guess the jokes on me now, huh?
*ducks & covers*

http://www.math.utah.edu/~alfeld/Eratosthenes.html

and http://mathforum.org/dr.math/faq/faq.divisibleto50 .html

After a little research I realize I had it backwards:

The American system is:
10^06 = million
10^09 = billion
10^12 = trillion
...

The European system (formerly used in Britain, still used in Germany)
is:
10^06 = million
10^09 = thousand million
10^12 = billion
10^15 = thousand billion
10^18 = trillion
10^21 = thousand trillion
...

What you fail to realize is that 1/6th of the probability is consumed by the Feyerabend Principle that balances out Bell's Theorem, that would otherwise lead to a probability surplus in the universe.

Okay, you're right. Here's a good page:
http://mathforum.org/dr.math/faq/faq.monty.hall.ht ml

1+1=2 anyone?

I'm sure that the average person doesn't know that either.

I'm trademarking "irrational" and "imaginary" because...well, you know..."real" is already taken.

i've never been good at math, so just _looking_ at this made my head hurt, so off to google i went...
after a number of very good sites that also made my head hurt, i found:
http://mathforum.org/dr.math/faq/faq.fractions.htm l/
which still made my head hurt, but at least i now understood the technique.

I thought I'd send a quick response to this. You can't get a nobel prize in Mathematics. I'm not sure if they could get one with this research for medicine though. I'm guessing it's that possible. Peace.

I thought I'd send a quick response to this. You can't get a nobel prize in Mathematics. I'm not sure if they could get one with this research for medicine though. I'm guessing it's that possible. Peace.

I thought I'd send a quick response to this. You can't get a nobel prize in Mathematics. I'm not sure if they could get one with this research for medicine though. I'm guessing it's that possible. Peace.

I thought I'd send a quick response to this. You can't get a nobel prize in Mathematics. I'm not sure if they could get one with this research for medicine though. I'm guessing it's that possible. Peace.

I thought I'd send a quick response to this. You can't get a nobel prize in Mathematics. I'm not sure if they could get one with this research for medicine though. I'm guessing it's that possible. Peace.

George Cantor established a Theory of Infinite Sets. So yes, there are an infinite number of rational and irrational numbers, but the infinity of irrational numbers is larger than the infinity of rational numbers. It's really only confusing if you assume "normal" (ie non-mathematical) definitions to commonplace words used in math.

up to a huge amount (10^39 I believe) here

Meanwhile, Duke Nukem Forever plans to number its first release i.

# cat /proc/cpuinfo
processor : 0
vendor_id : GenuineIntel
cpu family : 15
model : 2
model name : Intel(R) Pentium(R) 4 CPU 2.40GHz
stepping : 4
cpu MHz : 2412.523
cache size : 512 KB
fdiv_bug : no
hlt_bug : no
f00f_bug : no
coma_bug : no
fpu : yes
fpu_exception : yes
cpuid level : 2
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm
bogomips : 4784.12
# modprobe raid5
# grep 'MB/sec' /var/log/messages
Mar 10 14:12:18 xxx kernel: pIII_sse : 3092.000 MB/sec
Mar 10 14:12:18 xxx kernel: raid5: using function: pIII_sse (3092.000 MB/sec)

Lots of hardware RAID controllers use the Intel i960 as the embedded controller. I've read that 66MHz models are only slightly faster than a PII-400.

That was an interesting question... and the answer goes to:

Babylonians used base 60

Apparently they took the hexagon and observed that the perimeter is exactly 6 times the radius, so 6*60.

The first thing you to review is Combinations. A good write up on them can be found at http://mathforum.org/dr.math/faq/faq.comb.perm.htm l/

The the first I calculated was the total number of Combinations of 3000 Choose 120. This is the total possiblites the random algorithm can choose from. (It is pretty easy, just the size of the numbers are huge).

Next I assumed that it would be 3 songs picked from the same album of ten, which is 10 choose 3 (works out to be 120) and mutiplied that by the number of ways you can select the rest of the songs(2990 Choose 117). This gives you the total number of ways to pick the songs, while having 3 songs from that one album. I justed divide this answer with the previous one and came up with .005(Which should be the odds of selecting 3 songs from that one album). Which is a pretty big number if you think about it.