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marzojr wrote:
p4wn3r wrote:
I don't agree with him, but to be completely fair, I never found pragmatic arguments like this really convincing, because their premise generalizes to way too many things.
This may be a shocker for you, but the entire edifice of science is pragmatic: if something works and is useful, it is used; if it doesn't work or is not useful, it is discarded.
p4wn3r wrote:
For example, take Max Planck's case at the dawn of quantum mechanics
Here is a prime example of scientific pragmatism: the "trick" he used to fit the curve was done on pragmatic grounds ("it works"); it was later recognized as useful when Einstein used the idea to explain the photoelectric effect ("it works"), which ultimately led to quantum mechanics ("it works"). The entire rationale for accepting and using quantum mechanics is this -- "it works": it does a better job at predicting the outcome of experiments than the alternatives.
Likewise, special relativity was published by Einstein on pragmatic grounds -- Einstein himself knew that there were several problems on the foundations of special relativity that he could not satisfactorily solve at the time; he published it anyway because he judged it the only pragmatic way forward (again, "it works"). He latter addressed these issues in general relativity, but only after the insights gained from Minkowski about how special relativity make the world into a 4-dimensional space-time.
It is pragmatism all the way down.
That looks much better, your first argument was that one should accept doing something because the contrapositive would be dangerous. Just being picky, accepting scientific theories because they work is actually instrumentalism, so this is not really an argument to say that science is pragmatic, but since pragmatism uses instrumentalism, you don't get into much trouble.
marzojr wrote:
p4wn3r wrote:
We can't really know whether the behavior of the universe is independent of our perception because everything that we know from the universe comes from perception, and when your perception changes, you feel things around you differently too.
Meanwhile, the measurement instruments keep inconveniently measuring the same things and giving the same results regardless of your changes in perception.
Yet, two people can read two identical texts and interpret them differently.
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Warp wrote:
p4wn3r wrote:
For example, there's an ongoing debate discussing whether evolution is falsifiable
Is this an actual debate among scientists, or is it just creationists inventing problems that aren't there (and claiming that it's a "debate")?
It's among scientists and philosophers of science, according to the one semester course I've taken on epistemology. It'd be naive to say that creationists are not involved, but their interference there doesn't downgrade the issue.
As I said before, whether it's falsifiable or not is an extensive subject. I think it is, but I don't feel like elaborating or analysing it further, because unfalsifiability doesn't really mean it's non-scientific. Moreover, I think the increasing number of people who use Popper's dated and heavily criticized falsifiability to separate science keeps this discussion going on much more than creationist arguments.
It's actually natural that falsifiability is so popular among laymen and pop science magazines, because an elegant and short explanation is obviously much more appealing and convincing than a lengthy and extensive one.
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nfq wrote:
p4wn3r wrote:
His point was that using the term "science" to give more credit to spiritual knowledge implicitly implies that scientific knowledge is superior.
I know, and I like I said, I agree that scientific knowledge is superior to any "other knowledge", and I'm not sure knowledge is possible without science because science is a way of gaining knowledge, and I don't know any other way of gaining knowledge except by doing science. So, for example, if the people who created the ideas postulated in religions didn't do science to arrive at their conclusions, it's not knowledge, it's just speculation. But I believe they did do science, although it was mostly a science based on mind rather than matter. You might disagree that it's science, but they used the scientific method, so I think it's appropriate to call it science.
OK, we have to discern what we know from what's defined already. It's important to understand what concepts mean because otherwise you're unable to understand what people are saying or, in your case, fall into contradiction. I do not object to you saying "I believe this should be science because the accepted definition of science is flawed because of this, this and this". However, saying "This is science because it rejects realism" is like saying that 6 is an odd number because it leaves a remainder of zero when divided by 2. It simply makes no sense.
A similar thing refers to the world "knowledge". I encourage you to look for its meaning.
Bobo the King wrote:
I'm going to interject to say that a necessary (and perhaps sufficient) condition for a theory to be scientific is that it is falsifiable. If it isn't falsifiable, it isn't science.
I'm afraid it's not as simple as that. For example, there's an ongoing debate discussing whether evolution is falsifiable, one person brings up something that would kill evolution, and another one argues that it can still be fixed by something else, we could really go all day discussing this. I much prefer Kuhn's way of seeing science, he argues that science works based on paradigms that influence the way we interpret evidence (for example, when they believed planets moved attached to spheres, inconsistencies were resolved by adding more spheres to the model), until a time where the proposed model is such a monster that they discard it and use something else instead. This issue is known in philosophy as the "Demarcation problem" if you want to know more about it.
marzojr wrote:
The first bullet is just gravy; the second bullet is important, but it the last one that is the killer one (pun intended): if you assume that there isn't external world and act like it, but you are wrong, you can get severely injured or dead; if you assume there is an external world and you act like it, but you are wrong, nothing bad comes out of it.
I don't agree with him, but to be completely fair, I never found pragmatic arguments like this really convincing, because their premise generalizes to way too many things.
For example, take Max Planck's case at the dawn of quantum mechanics: "I can fix Rayleigh-Jeans law by instead of integrating energy, assuming it's quantized by the frequency and doing a series summation instead. I have no justification for its correctness instead of a mathematical trick to solve the problem." Publishing this (like he did) could get him strong criticism, while ignoring it wouldn't do any bad. So pragmatism can in some cases stall science.
Warp wrote:
One thing that in my opinion speaks a lot in favor of the world actually existing is that it behaves consistently.
The behavior of the universe is not dependent on your mental state. It doesn't matter if you are asleep, emotional, delusional, hallucinating, drugged, sick or mentally injured, the universe will still work in a completely consistent manner, as it always has. Imaginary worlds inside one's head do not behave even nearly as consistently, but their rules can change arbitrarily.
It is my understanding that one of the cornerstones of science was the realization that the universe behaves consistently. This idea has not always been as self-evident as it is today.
Interesting, I think idealism's biggest merit is not really if reality is a mind-generated thing, but that it's impossible to exist any knowledge outside of the mind. We can't really know whether the behavior of the universe is independent of our perception because everything that we know from the universe comes from perception, and when your perception changes, you feel things around you differently too.
Moreover, the human mind seems to have a framework that it must work within (perhaps this is even a requirement for survival). For instance, it retains pleasant experiences and blocks traumatic ones, it makes inductive reasoning extremely natural to us, possibly because we wouldn't be able to survive if this didn't come included in it. So, the way the mind is shaped greatly affects the knowledge inside it, but no mind is equal to another, so different people will think differently, so it seems reasonable to question whether knowledge is a universal thing. A crucial step to get out of depression is to actually realize that your thoughts are extremely affected by stuff you cannot control and that the horrible view you had of the world was caused by something inside your head that was created while you weren't paying attention.
I believe human knowledge is extremely based on human intuition, even the ones that are extremely formal. The postulates they have are accepted because they are intuitive and most laws derived from them are written only because it makes it easier to understand. At a higher level, we almost don't see things proved up to their formal threshold, but rather have intuitive explanations of the proofs. And formal sciences will greatly affect the way we formulate natural laws, so it's reasonable to believe that another civilization, whose minds work differently from ours, will deduce different natural laws.
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Warp wrote:
Isn't a more modern, semi-informal definition that entropy describes how much energy there is available for useful work in a system? The amount of such energy in a closed system can never increase (which is why it's impossible to have a perpetual motion machine that produces extra energy from nothing).
(Of course the problem with this definition is how do you define "energy available for useful work"...)
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nfq wrote:
marzojr wrote:
You also acknowledge in the process just how much important and useful you perceive science to be by trying to frame non-science as science
You seem to be implying that I'm somehow against science because I said that modern science is as good as ancient science.
I guess you also missed earlier when I showed that the so-called non-science (spiritual science) is more scientific than material science, because it makes less assumptions about the universe. Material science makes the unfalsifiable assumption about a world external to consciousness, while spiritual science doesn't make that assumption.
[omitted]
-- you are basically saying fields of knowledge are worthless unless they are science. Nice job :-p
So, don't you agree that fields of "knowledge" are useless unless they are science? What other systematic and reliable way is there to gain useful and accurate information about the world? How is anything "knowledge" if there's not some science behind it?
I believe you missed his point. He criticized you because the word "science" usually implies that the field in question accepts realism, so with this in mind, there can be no science that rejects the postulates that a common reality exists, natural laws exist, and they can be found using systematic testing (*). His point was that using the term "science" to give more credit to spiritual knowledge implicitly implies that scientific knowledge is superior. (Personally, I think saying that other fields are worthless just because of that term is kinda pushy, but it's what he said.)
It seems though that you have a conceptual problem here. "Knowledge" existing does not imply that there's a science behind it, whether non-scientific knowledge is useful or not is a matter of debate, sure, but that changes nothing about the concept. And Popper's falsifiability is not a line that divides science and non-science, it was brought up with this purpose but most philosophers today criticize it and seek alternative definitions. Most argue that it's a tough job to say whether evolution is falsifiable, for example, and that theories that are found inconsistent can be fixed by ad hoc hypothesis while still being considered scientific.
(*) If one's gonna be very picky, that requirement is not necessary. Formal sciences, like math, statistics and theoretical computer science say effectively nothing about reality, but their denomination as sciences is problematic from a philosopher's viewpoint.
EDIT: I don't know why the font is so large...
EDIT 2: Thanks, jimsfriend!
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nfq wrote:
Spiritual science once, and still does to some degree, let us explore illusive worlds of dreams and astral realms, but since most humans have lost the ability to control this ability properly, material science has given us videogames that can let us into these virtual worlds again, which will become more and more like reality in the future.
This is my favorite paragraph in the whole internet.
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sudgy wrote:
Of course even creationists themselves are unable to define the difference.
You're wrong here. Microevolution is when they change within the genetic code, macroevolution is when they add or subtract to the genetic code. There is a fine difference.
I've seen a little of genetics and unfortunately this is not correct. It's extremely common that people confuse "genetic code" with the information stored in the genes. The genetic code is nothing more than the relation between three nucleotides and the aminoacids they instruct to produce in the translation process.
Put it simply, where in programming you'd call a hello.cpp file the code, in genetics the genetic code is actually C++ syntax. The interesting thing is that the genetic code remains the same for most organisms, changes to it are very rare. Because of this, it's fair to expect that changes to the genetic code carry much less evolutionary significance than other processes, so it doesn't look like it should be the dividing barrier here.
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My attempt:
For 1 level, the minimum is clearly a1=1.
For n>1 levels, we necessarily have to load a state before the first level, that's because if you only savestate after the first level, you'll never finish the game at it.
So, we assume that for n>1, we have to use a savestate at the first level. We now try to reduce this problem to a smaller one. Suppose you partition the set of levels into two subsets A and B, and determine that you'll finish the game at the levels in A before the levels in B.
There's a simple way to do that whose optimality is probably easy to prove, you traverse all the levels in B in any order, savestate after that and do the optimal process for nA levels. After that, you load a state before the first level, traverse A in any order and do the optimal process for nB levels.
It should be clear that the amount of levels should only depend on the size of A and B, and seeing that traversing B, loading a state back to the beginning and traversing A takes n levels, the answer should be an = n + min(ai+an-i) for i = 1, ..., n-1
So, I can compute the first values, put them in OEIS, hope that someone studied this already and find https://oeis.org/A033156 , which luckily has a closed formula.
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Why is it now required that nominees for TASer of the year receive a rookie award or an award for a specific platform?
This makes perfect sense to me for the Best TAS award, since a TAS has necessarily only one platform, but TASers can work in many systems. For example, someone who's not a rookie could be the runner-up in all platforms and not get a nomination, when, at least for me, he/she could be a strong candidate for the award.
And to make it clearer, I'm not saying there's any unfairness with the current list, I don't think anything close to my example happened this year. I'm just asking what's the reason behind the change.
By the way, my votes go to Aglar, Ryuto, sparky and x2poet.
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arflech wrote:
Then the derived algorithm is f(x)=A*(1+1/x)/(1+1/X), which is indeed well-defined. However, is it strictly between A and AX/x?
It is evident that if x>0 then f(x)>A
Huh? The function in question was constructed having f(X)=A, having f(x)>A for x>0 makes no sense. For x>X:
x > X
1/x < 1/X
1 + 1/x < 1 + 1/X
(1 + 1/x)/(1 + 1/X) < 1
A*(1 + 1/x)/(1 + 1/X) < A
f(x) < A
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arflech wrote:
Also, although I can satisfy that functional equation with x*f(x) equal to a linear function, so that f(x) is of the form P+Q/x, this just brings us back, in the best case, to some weighted arithmetic mean of A and AX/x, which I have already shown to have a problem of lack of well-definition.
I'm not sure you quite understand well-definition here: The idea is that there's a set of values, and the easiest way to describe how to get them is to state the value at one point and use some algorithm to get the rest, and this algorithm is well-defined if and only if you get the same set of values regardless of the initial point. If you say that the unit price is A when the size is X, and your algorithm then says that the unit price is B when the size is Y and C when the size is Z (any distinct fixed values of Y and Z within range will do), and then I start that algorithm all over again by starting out with "unit price is B when size is Y," and I don't end up getting A with X and C with Z, then the algorithm is not well-defined, because the set of values you generate depends on the point at which you started generating them.
I do understand what you mean by well-definition. I'm just arguing that the problem of you getting different curves for different data is not related to the means themselves, but you evaluating them using different extremes. You're correct that simply using the extremes at a point (X,A) will yield different results, but in order to find a well-defined algorithm you don't need to explicitly consider them. You only need to consider the extremes at point (1, A')
Consider a different problem. The algorithm you want to build will receive only a real number A' and assume f(1)=A'. Because of this, it's easier to find a well-defined function, you just need to make sure f(1)=A'. For example, you can use the extremes f(x)=A' and f(x)=A'/x
Now, generalize to your problem. It receives two real numbers X and A, and assumes f(X) = A. This can be reduced to the previous one, pretend that instead f(1)=A' is given and use the same extremes: f(x)=A' and f(x)=A'/x. Now you can find this A' by solving f(X)=A. You don't even need to check if other points in the curve will give the same curve, because of the way it was made.
So, this leads us to the conclusion. Given f(X)=A, using a mean of extremes f(x)=A and f(x)=AX/x leads to a possibly not well-defined curve. However, using the mean of f(x) = A' and f(x) = A'/x and manipulating A' so that f(X)=A always gets a well-defined answer.
Is there any particular reason you need to explicitly consider the extremes f(x)=A and f(x)=AX/x to make a well-defined algorithm? It only seems to make things harder.
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arflech wrote:
Now what about well-definition?
It's because the well-definition of my example is based on the well-definition of a1, or in what you originally intended, it only works if the information you have is always f(1) = A. This might seem a strong assumption at first glance, but it's not. Solving the problem for an information at f(X)=A is not very different from solving it for f(1)=A.
It's basically: having observed f(X)=A, which value A' for f(1)=A' would give a curve consistent with f(X)=A?
For example, f(x) = A(X+1)/(x+1) for the harmonic mean and f(x) = A*sqrt(1+x-2)/sqrt(1+X-2) for the quadratic mean.
EDIT: The arithmetic mean will work for the additive property, I didn't see before because I switched letters here, it should be an's: xD
bn+1 = (bn + bn+2)/2
You can satisfy the functional equation with (x f(x))'' = 0 and f(X)=A
This should be f(x) = A(k/x + 1 - k)/(k/X + 1 - k), for k between 0 and 1.
It looks like anything that's f(x) = A g(x)/g(X) within the appropriate bounds works. It may be that, since the geometric mean makes f(x) a constant times a power of x, the division causes a shift in the function and the method you used ends up generating the same function.
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If I understand correctly your statement, that problem can be abstracted in the following way:
(an) is a sequence of real positive numbers that designates the price of a box of n oz, this sequence needs to be strictly increasing.
(bn) = (an/n) is the sequence of the unit prices, this one needs to be strictly decreasing.
The "additive property" would imply that this has to hold: bn+1 = (bn + bn+2)/2. This sequence has to be an arithmetic progression, but you require it to be bounded, so, it actually must be constant, and unfortunately that breaks it being decreasing, so no solution exists.
Ignoring the "additive property", we just need to satisfy these: an < an+1 and an/n > an+1/(n+1)
Or better: 1 < an+1/an < (n+1)/n
The geometric mean of the two extremes gives an/a1 = sqrt(n). That means an+1/an = sqrt(n+1)/sqrt(n), which does satisfy the inequality.
The harmonic mean also seems to be valid. an/a1 = 2n/(n+1). an+1/an = ((2n+2)*(n+1))/((n+2)*2n) = (n+1/n+2)*(n+1/n). n+1/n+2 < 1 and (n+1/n+2)*(n+1/n) > 1 implies n² + 2n + 1 > n² + 2n, which is true.
(Also, I've been assuming that you wanted a function whose domain is the entire set of the natural numbers, if your domain is actually a finite subset of them, e.g., 1 <= n <= 10^2011, it might be possible to satisfy your additive property)
P.S.: That's some unusual stuff to think while shopping for cereal...
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Well, the Philistines are the ones he battled against, and the battle was what ultimately led him to commit suicide. Also, at some point, Saul refused to follow God's orders, so possibly God might have left him on his own at that battle, which makes sense when that text says God wouldn't answer his prayers. Perhaps someone with more biblical knowledge can explain.
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pirate_sephiroth wrote:
Look at how many times could that Saul guy die, back in the day:
1SA 31:4-6 Saul killed himself by falling on his sword.
2SA 1:2-10 Saul, at his own request, was slain by an Amalekite.
2SA 21:12 Saul was killed by the Philistines on Gilboa.
1CH 10:13-14 Saul was slain by God.
Wut? Dude, they're just four passages describing Saul's death. Why do you think that if something is written four times it actually happened four times?
Anyway, if you're interested to know why they make sense you could start here: http://en.wikipedia.org/wiki/Saul#Battle_of_Gilboa_and_the_death_of_King_Saul
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That was interesting, Nach. My experience with UI can be summed up as:
* I don't remember windows 3.1 really well, I was 3 or something when I used it, I can only vaguely remember the look of the windows, a spaceship DOS game I played in it and a DOS program that my father used to register customers.
* Win95 was an enormous surprise to me and I can see why it was such a huge hit, I was next to my father when he installed it from 13 floppy disks and when it booted we were surprised that there was no need to type "win" in the DOS console to open the graphic interface.
* Win98 was basically the same thing in UI. At that time, my desktop was flooded with icons, because when I started using a program regularly I put it on the desktop and forgot to remove the others, as clicking on the icon was my main way of launching a program.
* I installed windows XP a lot of time after it was launched, so my hardware was well prepared for it and I didn't notice many performance drawbacks. I didn't notice much differences from its predecessors aside from the new theme, the win95 paradigm was still there. I changed the way I used the computer, I started opening the programs using the "Run" dialog and typing what I wanted.
* During the long development cycle of XP's successor, I eventually installed Debian and began dual booting Debian and XP. I loved Debian, it was the OS where I first became a "power user" and really started to understand computers better. From that on, I've always used Linux distributions with GNOME and have no experience with KDE, so I never experienced the change to KDE4, though I've heard a lot about it from others.
* I stayed a long time with XP and skipped Vista. Today, I dual boot win7 and Ubuntu (I switched to Ubuntu, because I thought Debian was too conservative and its updates lagged a lot behind, but lately Ubuntu seems to be rushing some releases, so I'll probably get back to Debian when Wheezy comes out).
The biggest annoyance I found in win7 was the new Control Panel, which is stupid. The best thing for it is the search feature in the start menu. It's very convenient, I start typing the name of the program and after a few letters its icon is up there for me to click.
Then 2011 came and GNOME 3 brought the most radical change to UI I've ever seen. It was completely absurd at its time, GNOME 2 was a windows 95 like environment that everybody loved, and suddenly it became a UI that had no minimize button in its windows, demanded a lot from hardware, and you had to hold Alt to bring the menu option to shutdown the computer.
It took me nearly one month using it to understand what the developers had in mind. Fortunately, with GNOME 3.2 things got a little more stable and now it seems GNOME plans to incorporate a lot of extensions that people developed for it in the main project, so it'll likely improve a lot in the future.
I think that the whole UI wars though are a bit overrated. There's an obsession with UI in every software project, and for me at least, there is a lot of stuff more important than it, people are always gonna complain if you change what they're used to, and given that I survived the change from GNOME 2 to GNOME 3, I think I can take whatever "unholy mess" the developers throw at me (this is not a challenge though ;) ).
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What I know is:
Emulation problems happen in both MMBN4 Red Sun and MMBN4 Blue Moon. However, they are more evident in Blue Moon because iirc there's an area where you'll get a black screen and a crash. However, if you use some Navi chips in both versions, a freeze will happen. I completed Red Sun on VBA and didn't notice any errors, but they appeared when I started messing around with it.
If you run them on a DS, you won't get crashes or freezes, but the game will be very slow where it was supposed to crash. I don't know about GBA-SP, I assumed it was functionally identical to the original. I know the DS uses a different BIOS.
Anyway, watching the submission...
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I define "minimally divergent" to mean that if we take any infinite subset of {an}, call it {ank}, then either sum({ank}) or its "complementary series", sum({an}/{ank}), must necessarily converge.
This says, for a given series, "every partition has property X", I want to disprove this, so I prove the opposite of this statement, namely "there's at least one partition that doesn't have property X". I only need to construct one example in order to do so. I didn't construct a subsequence that satisfies the condition, I constructed one that doesn't, i.e, both subsequences diverge.
EDIT: In case I still wasn't clear:
(S is "minimally divergent") iff (S diverges and every partition of S has property X)
The proof is: (S divergent) implies (S has a partition that doesn't have property X)
Thus, (S diverges) and (every partition of S has property X) can't both be true at the same time.
So, no minimally divergent series exists.
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Easy to understand, but not completely correct argument:
First consider only series of positive terms that diverge to infinity. Given any divergent series of this type an, we are asked to partition it into two other series ani and anj such that both diverge. The series will diverge if, for every real number K, there's a partial sum of it that will be larger than K. Obviously, if the series diverges, if we remove a finite number of terms from it, it'll continue diverging.
Now we have to partition it into two divergent series. First, you have an, and pick the number 1, keep summing the series until you exceed 1 (this will always happen because it diverges), put all these values in the sub-sequence ani. After that, you removed a finite number of terms of the series, it still diverges. So, starting from the first one you didn't remove, you keep summing the series until you exceed 1 again, and put all these values in anj.
Keep repeating this process with the remaining sequence. We now see that our method of construction can divide each subsequence we created in infinitely many intervals, each whose sum exceeds 1. So, given any real number K, we know there's a natural number n > K, and picking n of such intervals, we know that the sum of all of them will exceed n, and since n > K, will exceed K also. So, they both diverge.
Obviously, that doesn't solve the problem, because in order to diverge, a series doesn't need to be positive for every term or even its sum go to infinity ( (-1,1,-1,1,...) for example). So, we need to generalize this argument to account for the general case.
Proof:
By definition, a series diverges if and only if the sequence of its partial sums also diverges. Since the set of real numbers is complete, a sequence diverges if and only if it's not a Cauchy sequence.
So, with a divergent series an, there's an epsilon>0 such that for any choice of N>0, there are n,m>=N, with |a_n+a_(n+1)+...+a_m| >= epsilon.
We then partition the series like in the previous method. For a divergent series, we find any epsilon, N, n, m that satisfy the inequality and put all terms from a_1 to a_m in ani. After removing the finite number of terms, the inequality can still be satisfied with the same epsilon, since it must hold for all N>0. So, we find another n,m that satisfy the inequality and put all remaining terms up to am in anj.
After repeating this process indefinitely, we see that the two series have an infinite amount of intervals whose sum exceeds a given epsilon in absolute value, so the partial sums of both do not form a Cauchy sequence, and so they diverge.
This method is able to partition any divergent series in two diverging ones, so no series can "diverge minimally".
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This problem is actually a simple case of a well known computer science problem, which is determining if a perfect matching exists in a bipartite graph. You can look at Wikipedia for the terms.
If you treat the squares as dots and consider an edge as a line linking connecting each square to its neighbors, you have a bipartite graph, and a perfect matching problem.
The proof of impossibility relies on the fact that there can be no perfect matching in a graph if the number of elements in the two independent sets is different.
Intuitively, if you color an edge as black when it's matched, and as white if it's unmatched, you can visualize the matching, or better, the domino cover.
So, if you want to cover a board with two squares of different colors removed, you first take any matching in the complete board, probably the one where all dominos are in vertical position, because it's easier to see. Then, if you pick two squares of different colors, you can always find a path from the first to the second that consists of black edge -> white edge -> black edge -> white edge -> ... -> black edge. Then you exchange the colors of all edges in this path and remove the two original vertices, and you have covered the board without them.
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Flip wrote:
An 8x8 board has 2 diagonally opposite corners removed. Try to cover the remaining board with 1x2 rectangles, or prove impossible.
Simple. Color it like a chessboard. Whenever you place a 1x2 domino, you cover a light square and a dark square. However, to fully cover the board, you need to cover 32 light + 30 dark, or 32 dark + 30 light. Since the number of squares of the two colors is different, it's impossible.
