Honestly though, who cares? It's close enough. The only thing more purer than a Pure Mathematician is his virginity.
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Anonymous2009-01-21 2:37
You admit you need a maths genius to shut FrozenVoid up? You /prog/grammers are a bunch of fucking kids. Go back to your toy languages and SICP, you'll never amount to anything more than the code you write.
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Anonymous2009-01-21 3:58
>>7
You impertinent little shit. Guess who made the browser you just posted with, are the maths software you do your 1+1 bullshit with? That's right, PROGRAMMERS. Guess what egghead, there's more to life than memorizing equations that OTHER people came up with, you low life amphibian shit.
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Anonymous2009-01-21 4:01
>>8
Do any SKILLED programmers post on /prog/, or are you all just a bunch of ENTERPRISE MONKEYS?
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Anonymous2009-01-21 4:03
>>8
Seriously, us programmers are required to be flexible, constantly learning new technologies and paradigms. We invent stuff. What do you do? Learn equations and theorems WORTHY mathematicians invented, then drop out and take up Psychology or Political Science. Hahaha, here's a nickel kid (referring to >>7) go tell someone who cares.
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Anonymous2009-01-21 4:08
Mathematicians are truly the "copy cats" in the world. Think about, what do most maths graduates do? They either:
1) get a PHd and add some tiny, worthless new fact in the giant arena that is knowledge.
2) drop out see >>10
3) become elementary school/high school maths teachers, where they can regurgitate COPIED (STOLEN) information, where students can complete the cycle of doing either 1) 2) or 3)
They contribute NOTHING to the world. They are detached, sociapaths who's only shtick in life is being able to REGURGITATE some worthless, pointless little fact to try and impress people.
Attention:
YOUR PROFESSION IS WORTHLESS.
YOUR DEGREE IS WORTHLESS.
To paraphrase >>7
YOU'LL NEVER AMOUNT TO ANYTHING MORE THAN THE THEOREMS YOU MEMORIZE.
Honestly, gaiz. Most professional mathematicians (not the kind who drop out after they've learned all the maths their weak minds can handle, which incidentally is about the most that your average Ph.D student in CS knows) are quite useful people. And that's only talking about applied mathematics.
Who developed the counting numbers that you monkeys constantly use in your ifs, whiles and fors? Mathematicians. Who set the foundation for physicists to delve deeper into the physical world? You fucking guessed it. What did those physicists do after they took these mathematical tools and started quantizing nature? That's right, they figured out the atomic structure and even how to manipulate it. What else came next? Entire power grids, light bulbs, telephones, radios, you fucking name it. Only after your electrical engineers toyed around did mathematicians realize the potential of this technology to help in their calculations and theorems. Computer "scientists" were soon after a necessity to maintain these newly founded systems, but you know what? All the early computer "scientists" were just mathematicians. They birthed an entire technology. Mathematicians realized their creation had grown so large it needed it's own set of professionals to help sustain it while they fucked off and did obscure shit like write the algorithms you fucks MEMORIZE in your stupid classes.
Face it, you're our janitorial offspring.
Losers.
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Anonymous2009-01-21 10:58
"6. the division can be converte dto multiplication by inverse of 10 (1/10)
1/10*1/10*1/10*1/10*1/10...
7. the series don't have zero in the multiplication sequence and cannot be equal to zero"
dont bother with him, he's full of shit
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Anonymous2009-01-21 11:50
NERRRRRRRRRD WARRRRRRRRRRRR! XD
Mathematicians: Discover fundamental facts about the "world" which will be as true in 500 years as they are right now. The work of Gauss or Jacobi or Abel in the first half of the 19th century are still relevant to work being done today. How many physicists from that time can you say that about? Even the mathematicians whose work isn't terribly important has created something truly permanent for the world to remember him by, which is far more than just about anyone else in the world can say.
Programmers: Spend days in a dark room with one hand stuffed in a bag of doritos and one hand on their keyboard, coding greasemonkey scripts that make it slightly more efficient to surf their favorite discussion board and waste even more hours of their lives. Their work does not create fundamental human truth, it makes pixels on a monitor flicker in a certain pattern. Their work will be obsolete when the next version of Windows comes out.
I've been both a programmer (professional for 5 years) and a mathematician (currently grad student). Programming requires skill and a logical, organized mind, but in the end, no significant intelligence or creativity.
>>12
My question to you is, what have you contributed to this big field of maths? What was the last big contribution from maths which literally changed the way we live? You mathematicians remind me of the 80 year old baseballer, once famous in his day but now too old and decrepit to be doing anything useful. Instead, this old fart likes to remind people of how good he once was, instead of... you know, letting nature take its course and dying.
Face it gramps, you're finished. I would estimate 80% of maths graduates either change majors, or go off to become sales assistants or coal miners. Face it, you're our janitorial offspring.
I find this statement particularly interesting. Janitorial offspring, how quaint. You know, I couldn't agree more. We run the show now, pops. We create the software for the GPS in your car, the OS and software you use at home.
We quite literally rule the world.
>>14
Blah blah blah. I don't care about what those old farts did 500 years ago. Tell me, what are you contributing to the world right now, with your maths degree? What are you researching? What are you doing with your life?
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Anonymous2009-01-21 15:52
Ewwwww!! >>16 Just took a shit in >>12 and >>14's mouth!!
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Anonymous2009-01-21 16:25
>>16
Are you proud of the fact that you'll spend the rest of your life "inventing" software with a finite lifespan? Does making ripples in the sea amuse your small mind? Mathematicians will keep the world running. They'll keep drawing the blueprints, you'll keep building their brainchildren. You would be nothing without the equations and theorems we labor over. Thousands of lines of code? That's nice. Try wading in the waters of creative genius for a change. But you've been glued to your monitor for so long that you've forgotten what it's like to have a true spark of intuition.
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Anonymous2009-01-21 16:32
>>18
You haven't answered my question. You know it's rude to ignore somebody who asks you a question which you don't answer. I guess that's to be expected from a sociopath math weenie, strung out over sparks over intuition. Groovy man.
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Anonymous2009-01-21 16:45
>>19
I'm researching non-commutative geometries in string theory. Still reading SICP?
i was just making note of the use of "string theory" there. i like commutative algebra and algebraic varieties more, but i guess we could get along if we both worked with C* algebras.
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Anonymous2009-01-21 18:24
>>16
>what are you contributing to the world right now
Absolutely nothing. The math I do (elliptic curves/modular functions/etc..) has fuck all to do with anything in the real world, except possibly cryptography (but any cryptography based on prime numbers will be worthless once quantum computers are invented anyway).
What I AM doing, though, is contributing (in a tiny way so far) to the expansion of a field of knowledge that contains some of the deepest and most difficult truths discovered in the history of man.
>>24 What I AM doing, though, is contributing (in a tiny way so far) to the expansion of a field of knowledge that contains some of the deepest and most difficult truths discovered in the history of man.
Translation: I'm sitting up in my ivory tower contributing absolutely nothing tangible to the world
Maybe all you programmers and math people can clarify something for me. I've been considering majoring in CS, however, the question of it's academic content has bugged me. How much theoretical computer science does the average cs degree entail as opposed to coding?
From a philosophical viewpoint, stuff like questions regarding computability, Church Turing thesis, halting problem, etc. are very cool but how often does this stuff surface as opposed to time spent learning the idiosyncrasies of some language?
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4tran2009-01-23 17:09
>>36
I think it's variable, though a typical cs degree will probably be mostly coding. Most institutions give you enough flexibility for you to focus on algorithm theory if you're so inclined.
It can be proved for instance, that the best comparison based sorting algorithm is O(N log N).
People are still working out limits of quantum computing, etc.
Stay away from Scheme; it is terrible, except for comic value.
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Anonymous2009-01-24 11:12
Is it possible to add or subtract an infinite sequence?
Is 0.999... - 0.999... = 0?
You are able to manipulate recurring decimals in the same way as "normal" numbers, ie add, subtract, divide, multiply, exponentiate etc.
It is possible to define addition and subtraction, as well as scalar multiplication of infinite sequences, you get things called an l_p space, depending on what sequences you want, wikipedia it.
Infinity minus infinity is an indeterminate form. There is no answer to that.
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Anonymous2009-01-24 16:10
lol dongs
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Krieger2009-01-24 19:59
I can't believe anyone who has taken a math class higher than basic algebra still believe 0.999.... is not equal to 1. There are numerous proofs that they are equal. I'll give you a few basic ones to start.
1. Between any two non-equal numbers in the set of rationals, there lies an infinite quantity of numbers. What number lies between 1 and 0.999....?
2. Take 1 - 0.999..... and you'll get that it equals 0.000.....1, which exactly equals 0. So the difference between 1 and 0.999... is exactly equal to 0.
3. 1/3 = 0.333....
multiply both sides by three and you get
3/3 = 0.999....
1 = 0.999....
The whole thing seems obvious, even using 8th-grade level proofs....
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Krieger2009-01-24 20:01
>>42
K, switching between different windows and got my topics mixed up....meant to post in a different forum.
Don't know why you've quoted me in on that one, I agree his proofs are terrible, I'm trying to educate him about the ideas behind the proofs.
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Anonymous2009-01-26 21:45
As a sidelong and unassociated reply to the posts above, attacking and debating the utility of the most abstruse mathematics, without taking any any personal umbrage, and only as it is my pleasure...
Multivariable calculus put men on the moon, compact disc technology was only feasible with complex analysis, and number theory informed RSA encryption, which still plays a role today.
The point: contrary to mathematician G.H. Hardy's noble conceit that pure mathematics exists in a kind of "safe" vacuum, and cannot be applied for any special good or harm (The Bomb, and chemical weapons, derived via physics and chemistry, are the obvious Objects here), the historical trend is that even the most obscure mathematical truths will eventually be applied.
Math is the most useful of all, even if you haven't yet built up the hundred years of military industrial capital.
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Anonymous2009-01-26 23:12
Without computer losers, I would have to leave my apartment to find porn. Therefore programmers > mathematicians.
I don't know why I keep seeing the 1/3=.3333... proof, it assumes something that the opposing side believes to be false.
My own take on the topic is that the value of .9999... is something infinitely close to the number 1. The only thing that can be infinitely close to 1 is 1 itself. Thus, .9999... is just another way of saying 1.
Sage because I know nothing about math, and am just passing by.
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Anonymous2009-01-29 13:42
>>62
Your statement "I know nothing about math" is true. So why would you bother commenting.
The way we define decimal expansions ensure that 0.99... = 1, it's not even a matter of proof it's pretty much a matter of definition.
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Anonymous2009-01-29 22:25
>>62
Can't we just hope the other side dies out in a few years?
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Anonymous2009-01-30 0:06
>>64
I don't really think that's possible though. :/
It's like the gays. Obviously gays aren't having children, so they can't pass the gay gene on, but somehow there are still gays around. So even though all the gays that were around in, say, the 30's have died out by now, there are still gays around.
It's the same with programmers. They don't reproduce, but somehow they're still around.
Just as a little aside, for those who are interested, the troll from the OP is no other than FrozenVoid, who I believe /sci/ should know quite well. http://dis.4chan.org/read/sci/1172747610
So technically, this troll is /sci/'s responsibility. You made him, you clean him up /sci/
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Anonymous2009-01-30 1:11
>>67
Hmmm, so the troll started here, but moved on to more fertile trolling grounds, namely /prog/.
Interesting.
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Anonymous2009-01-30 2:16
>>40
If that was so 1-0.999...=undetermined, but its obviously equals 0
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Anonymous2009-01-30 3:31
>>69
Infinity minus infinity is an indeterminate form. There is no answer to that.
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Krieger2009-01-30 16:18
I'm going to give you several proofs here, and hold on a second, I want you to try something new. Instead of questioning the formality of the proof, explain why you believe it's incorrect.
1.
x = 0.999...
10x = 9.999...
10x-x = 9.999...-0.999...
9x = 9
x = 1
1 = 0.999...
3.
I wouldn't call this a proof, but I'd like you a non-believer to answer this question:
What number lies between 0.999.... and 1?
Seeing as you believe they are distinct, you should be able to answer this fairly simply.
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Anonymous2009-01-30 20:14
1. You haven't properly defined what the symbol 0.99... means, and thus cannot assume that algebraic manipulations (such as addition, multiplication) can be applied to it in any meaningful way.
2. You've defined it as a limit, that's at least a start, however you've applied a theorem on finite geometric series, as a limiting case, to this series.
This works, but you haven't proved that it does, so this one isn't a proof either.
3. As I said last time, this is the closest to a proof.
All that's lacking is you need to state what you're saying in a better way.
The real numbers are a hausdorff space, so given any two distinct points there are two disjoint open sets containing them. However for any open set containing 0.9999... it must have 0.9999.. + e for some e>0, but 0.9999...+ e > 1 for any e >0. Therefore you can't find two such sets, therefore 0.999.... and 1 aren't distinct points.
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Krieger2009-01-31 2:26
>>72
1.
I'm not sure what exactly you're saying here. By 0.999... I mean zero point nine repeating, 0.(9), etc. I'm not sure how else to define it.
2.
If I'm not mistaken, the sum of an infinite geometric series is:
(first term) / [1 - (common ratio)], which is the formula I've used. So I'm not sure what you mean by,"applied a theorem on finite geometric series."
>>73
I'm not sure how this is relevant to anything...
1. Well you have to define somehow, otherwise it's just a symbol, it has to have some sort of mathematical interpretation.
Generally you define an infinite decimal expansion 0.a_0a_1a_2..... to equal the limit of the infinite sum a_i*10^-i.
It's a pretty easy job to show this converges for all value of a_i. during this you'll prove a proof of the form of 2. ie that all numbers which have an infinite string of 9's in their decimal expansion have two equivalent decimal expansions.
The reason your proof of 2 doesn't work is because you're applied a result that is derived to work on finite series, and taken a limiting case.
For example apply your formula to the series 1 + 2 + 4 + 8....
you get the answer -1, nonsense (in a sense anyway). You have to prove that it still holds for any common ratio < 1.
Now once you've prove all this you can start proving that addition and multiplication work for decimal expansions in the way you imagine (ie. that the new series you get still converges and converges to the value you want) and is well defined (ie, if you have A=A', B=B' for equivalent decimal expansions then c*A = c*A' and A+B = A'+B')
Then you can apply your second proof.
tl;dr? Maths is harder then you think.
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Anonymous2009-01-31 9:55
Maybe your third proof attempt can be turned into a proof.
Informal proof sketch/idea for #3.
1. Fact: a real number is uniquely described by a finite sequence of digits, followed by a decimal separator, followed by an infinite sequence of digits
2. Fact: The amount of real numbers is uncountably infinite.
3. We can define the successor function s : R -> R for real numbers as follows: Let "x.y" be a representation of a real number, where x is a finite sequence of digits, and y is an infinite sequence of digits. Then s(x.y) = x'.y', and x'.y' are obtained by incrementing the last digit of y.
(It should be provable that from this definition, for all reals x.y, x.y <= s(x.y); and also any real is s(s(s(...(0.0...)))...), i.e., some above-infinite amount of applications of the successor function)
2. If 0.999... != 1, then by (2) there should be an uncountably infinite amount of numbers between 0.999 and 1.
3. But s(0.999...) = 1.
4. (2) and (3) form a contradiction. Hence 0.999... must be 1.
>>82
I only come here from /b/ now and then to point out how retarded u gaiz are, so I don't know about your fancy bbcodes.
/irony
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Earth2009-01-31 20:49
>>77
1. Fact: Wrong.
2. Fact: True, better then the last fact at least.
3. Wrong, wrong and wrong.
2. How the fuck did you go back to 2? Anyway, this point does not follow from 2 in any logical sense, it's true, but faulty reasoning.
3. No. 0.999...=1 without any sort of successor function
4.Just what the fuck.
You seem to have assumed the reals are countably infinite, to be able to inductively reach any of the from this silly "sucessor" function, which makes no sense anyway.
How can you increase the last digit of an infinite sequence?
What s(pi)?
To repeat, Maths is harder than you think.
And I call it maths because it's a series (multiple) of interwoven disciplines. And also cause I'm a eurofag.
look it up bitches, 0 is the only infinitesimal number in the reals. if you want to work with infinitesimals, fine, you better get used to some of the following ideas
x^n = 0 does not imply x = 0
it is possible that two numbers are neither equal nor not equal.
>>98
I'm not sure why this was directed at me....All I was asking about was what (1/3...) meant, particularly the ellipsis. I completely agree with your line of reasoning.
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Anonymous2009-02-04 20:41
100 GET
God damn, /sci/ never changes.
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Anonymous2009-02-04 21:11
>>101
It wasn't disproven, just based on a fact that isn't accepted by the unenlightened.
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Anonymous2009-02-04 21:23
that because .999 is an approximation of 1/3 so .999 is an approximation of 1 therefor does not equal 1 but is an approximation.
After all, infinity was only formalized more than 50 years ago for most of its forms, and up to 150 years ago for the oldest. And that no common definition of real numbers see a difference between the two.
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Anonymous2009-02-07 4:52
>>99
So you finally admit you don't know what your talking about.
I rest my fucken case.
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Krieger2009-02-08 4:35
>>108
No, I'm actually fairly sure I said nothing to imply that I don't know what I'm talking about. I asked what (1/3...) means, as I'm fairly sure the ellipsis is meaningless, and I didn't say that RedCream's proof was a proof, I just agree with the particular line of reasoning.
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Anonymous2009-02-08 18:35
basically all rationals can be written as a fraction or in a decimal form which eventually terminates or recurs. and vice versa.
>>113
Splitting hairs here. It's just an analogy. Fine. .999... is a completely full glass of a substance that can be divided into infinitely small parts. My point is IT'S STILL EXACTLY ONE (as in 1) GLASS.
With every decimal place completely full no finite number can be added to .999... without it making more than 1.