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Any good sites, analysis practice?

  1. Mar 4, 2007 #1
    my text introduces topics briefly and if so, they give examples either way to easy or way too difficult and then only one example.
    how do/did you practice with specifically set theory?
    other types of math you can do a bunch of examples but with proofs it's so independent(to me, not you of course)
    i can learn and memorize all the methods and vocab
    but i can't seem to prepare for an exam since i'll be hit with a ton of unknown examples i have to race to prove while i examine it at the same time
    very short time for things that take a long time to do(once again for me not you)

    anybody know of any good sites where they lay down a question and then give examples of how go about proving it

    i want to practice with this, but I don't even know how to because my text is so vague

    (to all you arrogant bastards who flood this forum. it's of no use if you come in here to tell me how childish this is or how skillful you are. if my question is scatterbrained and doesn't make sense, then don't bother answering it)
  2. jcsd
  3. Mar 4, 2007 #2


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    This seems like a bit of a weird approach to me; asking for help with your studies, and then slagging off anyone who would think about helping you!

    Anyway, back to the question, you say you want to find somewhere with practice problems, but what specific topic are you after? For example, you mention "set theory" but then your title is "analysis." Perhaps you could post one of the examples from your text-book to enable someone to know what precisely you are looking for?
  4. Mar 4, 2007 #3
    it's preemptive strike for every other post i've left
    sometimes in the mist of insults you can still pick out some value

    i'm not really looking for 1 example
    i was wondering if anybody knows a site were they lay down various methods to proofs
    involving things from
    ---basic set operations---
    -containment, subsets, elements,indexed families
    ordered pairs
    (a,b) = {{a},{a,b}} -> i wouldn't mind examples with that

    functions etc.

    power sets

    i don't really have any specific examples
    that's my problem...i'll try and dig up some examples
    i just want more information but in depth and when it comes to proofs i'm curious to see various appraoches

    is this the wrong thread?
    my apologies
  5. Mar 4, 2007 #4
    I doubt you can find a website that will do a really good job of setting these things up properly. You'll probably have to go to various sites and piece everything together. It'd be much better to get a book from your library. The other thing is you're going to need a solid foundation in first order logic to do any of the proofs.

    For an analysis course you generally don't need to know how to prove these results but you should know them.

    Is this for your own initiative or do you need this for a course?
  6. Mar 4, 2007 #5
    a little bit of both

    i'll just pick random problems from the book
    (because after trying to figure them out I never really know if what i did is even correct)

    1)Let R and S be relations on a set A. Prove or give counterexampe
    a) if R and S are reflexive, then R intersect S is reflexive
    b)same for Union
    --a)in my very beginner like stupidity
    maybe i can say R is times 1 and S is minus 0
    so xRx and xSx seperately are reflexive?
    if x is in R intersect S then xRx is and so is xSx
    i dont know, i'm lost. is there a counterexample?
    am i even interpreting this question correctly
    --b)i thought i understood the union but in the end i was over analyzing it. this is something I can't afford to do.

    2)suppose f:S-->S for some set S. prove
    a)if f of f is injective, then f is injective
    b)if f of f is surjective, then f is surjective
    these appear straight forward until i think about them
    ---a)i don't even understand how that would work
    maybe i decide S is the set of all natural numbers(which still wouldn't get me far overall)
    maybe a,b, and c are subsets of S
    so f(a) is b and f(b) is c
    ...then i loose track and realize everything i'm thinking is stupid and i'me getting nowhere fast
    (on exams i get taken down similar paths by the time i realize i'm wrong i dont have time to do any other problems)

    3)Prove: if S is denumerable, then S is equinumerous with a proper subset of itself.

    these problems were chosen randomly by which had the least symbols
    it seems the more and more i do and study with this stuff the more and more lost and confused I get
    How do people study this, i have no approach
  7. Mar 4, 2007 #6

    matt grime

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    Read Polya.

    The place to start is 'with the definitions'. What is the definition of a reflexive relation?

    And the reason people get offended with answers here is because the answers are almost always 'just read the definitions', and they don't like that answer, and we don't like having to give the same advice every time.

    All of the above questions are immediate from the definitions of the objects in question. That isn't arrogance, that is just a straightfoward observation and there are no two ways about that. So what are the definitions of the objects?

    Take the ff question. If f is not injective, then there are x=/=y with f(x)=f(y). But then ff(x)=ff(y), so ff is not injective, thus ff injective implies f injective. See, it is a one liner. It is not arrogance that makes it a one liner. So stop moaning about the help you get and learn it (and no you wouldn't have got a response like this if you'd not been such a whinger; as I'm sure has been explained many many times, when someone says that something is easy and obvious it means, in respect of mathematics, which means it may take several hours for you to figure it out).
    Last edited: Mar 4, 2007
  8. Mar 4, 2007 #7
    you're absolutely correct
    i can't expect somebody else to explain things to me
    i can only explain it to myself
    it's stupid to complain
    maybe i'll come back when i'm good enough to actually formulate a logical question
  9. Mar 4, 2007 #8


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    You seem to have a lot of negative thoughts flowing around.

    I'd work on that first.

    The people at PhysicsForums are great in every way from school work to philosophy of life. You started taking shots at the members in the opening thread and now you're ending the thread with taking shots at yourself.

    Stop dwelling on the negatives and focus on the positives, however small they may be. I ate a tasty cake today. :biggrin:

    The best advice to solving bad textbooks is to find a new one by going to the library.
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