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Show that sup(A+B)=sup(A)+sup(B) and inf(A+B)=inf(A)+inf(B)

I'm trying to break it down to arbitrary elements. In order to add sets they have to have the same cardinality right? I was going to let the sets be countable, but then I read that A and B are subsets of the Real numbers.. so I can't do that since R is not countable...

so... any ideas?
 
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nvm, i got it.. just had to break down the sets into and arbritary elements and then do a double inequality..
 
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incase anyone was curious... (which I doubt, but eitherway)


also, for those that can dig it, here's some of the neat double integral stuff we are doing with polar coordinates..


to everyone else, sorry for posting yet another math thread here, haha.
 
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Smalls, with that double integral stuff you can derive where all area formulas come from. Then in calc3, you can do the same with volume formulas.

Yea, I dig it.

Did you figure out the trick on how many petals you will get on the flower by just looking at the formula? If not I'll have to dig up my old notes and look it up for you.

Another thought, knowing polar is awesome. It'll make life easier when doing anything with circles.
 
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That graph looks like the hybridization diagrams I was looking at...

Which math is this?
Is that abstract algibra?
The first bit is from Set Theory.
The second is calculus using polar coordinates. (Polar Coordinates is an alternative way to graphing. Basically you are graphing a radius with respect to angles) You're probably fimilar with sine and cosine functions right? Well, if you were to graph cos(theta) in polar coordinates, youd get the unit circle (instead of having to using y^2+x^2=1, which is why it is SO much easier) What the calculus is doing is finding the area that is inclosed by that function under another function...
 
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Smalls, with that double integral stuff you can derive where all area formulas come from. Then in calc3, you can do the same with volume formulas.

Yea, I dig it.

Did you figure out the trick on how many petals you will get on the flower by just looking at the formula? If not I'll have to dig up my old notes and look it up for you.

Another thought, knowing polar is awesome. It'll make life easier when doing anything with circles.
Yeah, I'm really digging this double integral stuff. At first I was freaked cause I suck at integration, but it's pretty cool.

Yeah, my prof last year drilled all the 'petal tricks' into our heads. It actually saved my ass today.. I had to write a quiz on finding the area enclosed by cos(4theta) and I remembered that it would have 8 petals. I looked over and saw a physics student sweating trying to put values through his graphing calculator to get an idea of what the thing looked like.

so far we have only worked with cosine functions though.. I guess it is because with sine you don't get a petal that is bisected by the 'x' axis. Yeah I always found polar and parametric functions to be pretty rad. Of course, I totally forget how to do parametric now...
 

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Man I'm glad I don't have to play around with double integrals and polar at the same time. Not too bad by itself but my professors always threw some nasty equations at us.
 
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Man I'm glad I don't have to play around with double integrals and polar at the same time. Not too bad by itself but my professors always threw some nasty equations at us.
yeah, my calc prof right now is pretty fair. He goes SUPER fast and expects us to know a lot, but his midterms are always very predictable and fair. He gives us mock midterms before that end up being very similar to the actual midterms. Therefore, the students that are good at calc get great marks and even those that arent so good at it but put the time and effort into studying and working on his mock midterms get decent grades too. I had 100 in the course but was sick as dog with only a few hours hours of sleep when I wrote the second midterm and ended up getting 90 on it... may seem silly, but I was pissed. They were all really really stupid mistakes, obviously the result of the lack of sleep.
 

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You're taking a class in only set theory?

The only set theory I've covered was in this proofs class I'm taking, where we prove conditional statements and some other stuff, but really we only covered it in passing.

When do you cover triple integrals? You end up deriving the volume of a sphere which I always thought was rad.
 
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You're taking a class in only set theory?

The only set theory I've covered was in this proofs class I'm taking, where we prove conditional statements and some other stuff, but really we only covered it in passing.

When do you cover triple integrals? You end up deriving the volume of a sphere which I always thought was rad.
Yeah, it's only set theory. Prove by induction is only a small small part of it. We've worked with logical implications, set arithmetic, set cardinality, induction, convergence, mod function, countable and uncountable sets, finite and infinite sets, supremum and infimum of sets, relations, functions... etc,.

you dont need a triple integral to the find the volume of a sphere. whatch the first video I posted.. I havent worked with triple integrals yet, but probably soon.
 

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Probably about as much as you. We spent a lot of time learning how to use PowerPoint and Excel. The course was a joke but I landed a good job with it and bought my first home at 27.
 
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The easiest way to do volume is with a triple integral. If you understand doubles, just throw another integral in front with a dz to match with it. I'm really busy today, but sunday I should have time to dig up some of my notes for you. Parametrics come in handy when those ****ing functions show up like hyperbolas. Calc3, you'll be able to integrate between functions such as 3d hyperbolas and such. I haven't done it in a while but it'll come back to me eventually.

There is some claus about what happens with cos and the petal ****. I'm pretty sure it shifts the whole graph around and kills the dissection aspect of the formulas, like you said.
 
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You're taking a class in only set theory?

The only set theory I've covered was in this proofs class I'm taking, where we prove conditional statements and some other stuff, but really we only covered it in passing.

When do you cover triple integrals? You end up deriving the volume of a sphere which I always thought was rad.
Calculus 3.

Here, integrate this on your own and you did calc3.
(pretend [ is an integral sign)



Integrate:
pi/4 pi/2 1
8 [ [ [ dr dro dtheta
0 0 0


Think of splitting the sphere up into 1/8's and you'll see where I got my limits and where that 8 came from. :)
 
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