Results 1 to 3 of 3

Math Help - Closure of sets

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Closure of sets

    A function f with domain (0,\infty) and co-domain R is log-like if
    f(x+y)=f(x)+f(y)

    Show the set of all log-like functions is closed under addition

    Attempted Proof
    Let functions f and g be log-like
    Consider f+g

    f(xy)+g(xy)=f(x)+f(y)+g(x)+g(y)<br />
    (f+g)(xy)=(f+g)(x)+(f+g)(y)

    Thus this set is closed
    Is this operation correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Haven's Avatar
    Joined
    Jul 2009
    Posts
    197
    Thanks
    8
    The top equation should be f(xy) = f(x) + f(y). Then your proof makes sense since (f+g)(x) = f(x) + g(x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    Actually your proof is a bit unclear. I think the following is better (using what Haven said):

    (f+g)(xy)=f(xy)+g(xy) = f(x)+f(y)+g(x)+g(y)=f(x)+g(x)+f(y)+g(y)=(f+g)(x)+(  f+g)(y)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Interior, Closure and Boundary of sets
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 18th 2011, 11:48 AM
  2. closure sets
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 27th 2010, 10:15 AM
  3. Convex Sets - Interior and Closure
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 2nd 2009, 04:03 AM
  4. Interior, Boundary, and Closure of Sets
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2009, 04:01 PM
  5. closure of sets (topology)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 17th 2009, 06:38 AM

Search Tags


/mathhelpforum @mathhelpforum