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Property of a sequence for a function.

  1. Aug 20, 2011 #1
    Ok so the ideea of the proble is the following.F:A->B....where A={1...k} and B={1...n}.The problme is divided in 2 parts.
    The first part of the problem asked me to write in terms of k and n the formulas for the number of functions,number of injective functions,number of increasing functions...etc.I've done that.What I don't understand is part 2 because the description is confusing for me.
    Part two states the following:"For each of the type of functions from part a) describe the coresponding property of the sequence {f(1),......,f(k)} for a function f of that type."
    Does this mean to show what it means to be a function,then an injective function and an incresing function and so on?
    Appologies if this question is ridiculous.
     
  2. jcsd
  3. Aug 20, 2011 #2

    micromass

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    Yes, they're just asking you to say what it means to be injective, increasing, etc. But you must phrase it in such a way to have a statement about {f(1),...,f(k)}.

    For example, you could say that f is injective if f(a)=f(b) implies that a=b. But that is not a statement about {f(1),...,f(k)}. The statement we're looking for is that {f(1),...,f(k)} are k distinct values.
     
  4. Aug 20, 2011 #3
    Can I say the following?
    Let A={1...k} and B={1...n} then a function is defined as:f(A):={f(a)|a belongs to A}
    And for injective functions f(a)=F(b) if a=b
    or should I just say that f(1)=......=F(k) if 1=....=k
     
  5. Aug 20, 2011 #4

    micromass

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    No, try to say only something about the set {f(1),...,f(k)}. What do you know about this set if f is a function?? Injective?? Increasing??
     
  6. Aug 20, 2011 #5
    that 1=f(1),2=f(2)...........n=f(k)
    f(i)=f(j) where f(1)=<f(i)=<f(j)=<f(k) if i=j 1=<i=<j=<n and
    f(1)<f(2)<f(3).....<f(k).....if 1<2....<n
    is this correct?
     
  7. Aug 20, 2011 #6

    micromass

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    for what is that an answer??
     
  8. Aug 20, 2011 #7
    Function: 1=f(1),2=f(2)...........n=f(k)
    Injective: f(i)=f(j) where f(1)=<f(i)=<f(j)=<f(k) if i=j 1=<i=<j=<n and
    Increasing: f(1)<f(2)<f(3).....<f(k).....if 1<2....<n
    is this correct?
     
  9. Aug 20, 2011 #8

    micromass

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    The function bit is not correct.

    If f is a function, what can {f(1),...,f(k)} be?
     
  10. Aug 20, 2011 #9
    the range.
    Are the other parts ok?
     
  11. Aug 20, 2011 #10

    micromass

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    Yes, that seems good.
     
  12. Aug 20, 2011 #11
    should I write the function bit like this 1->f(1)....?
     
  13. Aug 20, 2011 #12

    micromass

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    that would be better
     
  14. Aug 20, 2011 #13
    ok ....thank you
     
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