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On October 26 2012 00:59 Toadesstern wrote:
TL doesn't allow homework threads right? Is it alright to casually ask something really easy pregame in a mafiathread? :p Would be a oneliner if someone knows the answer.
///Edit: Screw this here we go:///
If M :={} there surely is no Maximum or Minimum (german terms, I guess they're the same in english?) because those have to be within M, but do sup(M) and inf(M) exist?
Obviously those two don't have to be within M which makes it possible in theory but is it really that way? As far as I know the definition is somewhat along the lines of:
There's an m in M for every s+E no matter how small I pick E. Obviously the other way around if you're looking at sup(M).
s doesn't have to be within M as already mentioned but m within M obviously has to be within M so there's no m I could pick as M = {}.
But than again I could easily just say "herpaderpa, I pick number x. No matter what m out of M you throw at me it won't be bigger/smaller than my x because there's no m in M!
Therefore M has to be confined/restricted (WHATEVER the term in english is... you get it, right?), therefore sup(M) and inf(M) have to exist according to definition."
I'd say there's no sup/inf because of the definition but my poor-mans logic sounds pretty much like I might be wrong.
S&B you're the fancy Cern-guy, surely you should know this :p
I did a quick Wikipedia check on the matter and I don't think an infimum and a supremum of an empty set exist, because they would have to be elements of the set.
http://en.wikipedia.org/wiki/Infimum
http://en.wikipedia.org/wiki/Supremum
Also, it would surprise me if a CERN guy would use set theory on a regular basis 
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On October 26 2012 01:23 KharadBanar wrote:Show nested quote +On October 26 2012 00:59 Toadesstern wrote:
TL doesn't allow homework threads right? Is it alright to casually ask something really easy pregame in a mafiathread? :p Would be a oneliner if someone knows the answer.
///Edit: Screw this here we go:///
If M :={} there surely is no Maximum or Minimum (german terms, I guess they're the same in english?) because those have to be within M, but do sup(M) and inf(M) exist?
Obviously those two don't have to be within M which makes it possible in theory but is it really that way? As far as I know the definition is somewhat along the lines of:
There's an m in M for every s+E no matter how small I pick E. Obviously the other way around if you're looking at sup(M).
s doesn't have to be within M as already mentioned but m within M obviously has to be within M so there's no m I could pick as M = {}.
But than again I could easily just say "herpaderpa, I pick number x. No matter what m out of M you throw at me it won't be bigger/smaller than my x because there's no m in M!
Therefore M has to be confined/restricted (WHATEVER the term in english is... you get it, right?), therefore sup(M) and inf(M) have to exist according to definition."
I'd say there's no sup/inf because of the definition but my poor-mans logic sounds pretty much like I might be wrong.
S&B you're the fancy Cern-guy, surely you should know this :p I did a quick Wikipedia check on the matter and I don't think an infimum and a supremum of an empty set exist, because they would have to be elements of the set. http://en.wikipedia.org/wiki/Infimumhttp://en.wikipedia.org/wiki/SupremumAlso, it would surprise me if a CERN guy would use set theory on a regular basis
they don't have to be part of the set, do they?
For example sqrt(2) can be a inf or sup for M if M = Z or N (the numbers Z or N, only have normal letters here...)
sqrt(2) isn't within Z or N but can still be sup or inf.
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So I actually didn't do any set theory in physics classes, and only a little bit in math classes. Actually most of the set theory I did was in a philosophy class.
So intuitively, I want to say there's no sup/inf - if the sup is the "smallest upper bound" or the least element of any given superset of M (bigger set which includes M as a subset) which is greater than or equal to all elements in M, then for M={} it's impossible to be greater than or equal to an element of M because there aren't any.
But I don't actually know, so I went to look it up, and I think it might be a matter of convention - Wikipedia says "If, in addition, we define sup(S) = −∞ when S is empty and sup(S) = +∞ when S is not bounded above, then every set of real numbers has a supremum under the affinely extended real number system." - implying that we have to agree to define sup({}) to be something or else it is undefined.
Yeah so intuitively I agree with your reasoning but if someone else here actually knows set theory then they should definitely chime in.
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oh wait I have an idea
The sup of a set doesn't have to be in the set, but it has to be in some superset which includes the set in question and is also defined, right? So the sup of the negative real numbers has to be a real number, but it's 0 which isn't a negative real number; the sup of the set of all buildings less than ten feet tall is a ten-foot-tall building, which isn't in the set but is a building, etc.
So if you're just saying "Sup({})" then I don't think it can be anything unless you define it by convention.
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I wasn't going to post this in the thread, but since we're talking about it anyways, and because i'm board, my logic is as follows:
my definitions of inf and sup are
given: x is a vector in Omega, f is a function which takes vectors from Omega to scalar values
inf f(x) = GLB{f(x) : x in Omega}
sup f(x) = LUB{f(x) : x in Omega}
so i'm assuming that M must be a scalar in your problem?
anyways, in order to evaluate GLB and LUB, you need to build a ball around any point in question. that implies that you need at least one point in the set you are evaluating. since you don't have any points, you can't evaluate inf or sup, as according to your definitions of inf and sup, you need to build a ball.
i think. or something about bananas.
e: my notes are for vectors of real numbers of an arbitrary size. however, you can still extend it to whatever, as long as you still have some metric for evaluating GLB and LUB. In order to evaluate any metric, as far as I know, you need to have a non-empty set.
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I am going to predict that I am going to be cursed with forced inactivity because:
a) Discussions are going to occur during my lectures and discussions.
b) None of my classrooms have reliable internet.
Edit: What is with all the math in the thread?!?!? Makes me sadness. Thread needs more English majors.
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The problem I've got is really that the existence of sup and inf is defined by whether or not something is bound or not (thanks to s&b for that vocab^^).
I'd say M={} is bound with my poor mans logic and therefor there has to be a sup(M) or inf(M) without knowing it (maybe some bullshit like everything in R, Q, C, N, Z or whatever you're talking about?).
Anyways it's probably some definition bullshit I could find in some textbook I guess.
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Open sets are, by definition, not bound. I would argue that the empty set is open, and therefore not bound. inf() and sup() only have meanings on bounded sets, therefore the empty set cannot have inf() and sup(). I'd go with that. I should ask my math prof what he thinks, make for an interesting conversation.
glhf
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On October 26 2012 03:16 ghost_403 wrote:
Open sets are, by definition, not bound. I would argue that the empty set is open, and therefore not bound. inf() and sup() only have meanings on bounded sets, therefore the empty set cannot have inf() and sup(). I'd go with that. I should ask my math prof what he thinks, make for an interesting conversation.
glhf
This seems to be what I remember from Math as well. But there was that time where I decided to do History/Philosophy/English instead of physics as my major so its been a while.
Edit: No Brows, don't you worry. I just got out of poetry class. I'm right there with you.
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I have a feeling this is going to be a spam fest though.
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Nope. I see math and calculations.
Not here. Not today.
![[image loading]](http://i.imgur.com/HIaqU.png)
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TOO MUCH MATH
WE NEED MORE PONY
![[image loading]](http://30.media.tumblr.com/tumblr_lk22cgTEn11qincmao1_500.jpg)
Mr. Mod, the game starts tomorrow am I correct?
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On October 26 2012 04:09 BroodKingEXE wrote:
I have a feeling this is going to be a spam fest though.
Gonzaw and Toad in the same game. Of course it will. Also, this is the first time I've played with either of them since my first ever game. I'm also quite verbose; often middle of the pack for post counts. We dont have too many of the usual lurkers either. I expect to be inundated with posts and I hope that the newbs keep up (lord knows I failed at it in my first game which was a mini...).
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I already said I'm going home on friday (about 15:00 my time, got to hand in my ana homework at 13:00...) and will prooobably hang out with family and friends. Visit my somewhat newborn niece and so on. Yeah I'll post stuff but not as much as usually :p
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On October 26 2012 04:37 drazak wrote:
I guess I'll /in on this
a little late buddy. You could /in as replacement though.
+ Show Spoiler +Sorry for calling you scum in obs qt so much, good thing you blue slipped (though I would probably still have lynched you)
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T_T Didn't look like the count was full, not sure if I want to be a replacement (probably won't read the thread if I'm not in it.
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On October 26 2012 04:25 Promethelax wrote:Show nested quote +On October 26 2012 04:09 BroodKingEXE wrote:
I have a feeling this is going to be a spam fest though. Gonzaw and Toad in the same game. Of course it will. Also, this is the first time I've played with either of them since my first ever game. I'm also quite verbose; often middle of the pack for post counts. We dont have too many of the usual lurkers either. I expect to be inundated with posts and I hope that the newbs keep up (lord knows I failed at it in my first game which was a mini...).
I dont know why they get such a bad rap, others spam much more than them. (This is not incentive for anyone to start trying to spam more)
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On October 26 2012 04:54 BroodKingEXE wrote:Show nested quote +On October 26 2012 04:25 Promethelax wrote:On October 26 2012 04:09 BroodKingEXE wrote:
I have a feeling this is going to be a spam fest though. Gonzaw and Toad in the same game. Of course it will. Also, this is the first time I've played with either of them since my first ever game. I'm also quite verbose; often middle of the pack for post counts. We dont have too many of the usual lurkers either. I expect to be inundated with posts and I hope that the newbs keep up (lord knows I failed at it in my first game which was a mini...). I dont know why they get such a bad rap, others spam much more than them. (This is not incentive for anyone to start trying to spam more)
For me at least they are the spammiest players I have played with. (Not counting Kush) but their spam also includes a lot of actual thought where as Kush's is all one liners.
Also they admit to it. Which makes it easier to call them out for it.
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United Kingdom36161 Posts
On October 26 2012 04:54 BroodKingEXE wrote:Show nested quote +On October 26 2012 04:25 Promethelax wrote:On October 26 2012 04:09 BroodKingEXE wrote:
I have a feeling this is going to be a spam fest though. Gonzaw and Toad in the same game. Of course it will. Also, this is the first time I've played with either of them since my first ever game. I'm also quite verbose; often middle of the pack for post counts. We dont have too many of the usual lurkers either. I expect to be inundated with posts and I hope that the newbs keep up (lord knows I failed at it in my first game which was a mini...). I dont know why they get such a bad rap, others spam much more than them. (This is not incentive for anyone to start trying to spam more)
gonzaw doesn't really spam, but he does post an epic amount. Which makes it all the more scary.
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EPT
