Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Set of functions that is eventually zero

  1. Oct 5, 2012 #1
    Usually, in homework problems, I come across something like, "Let [itex]F[/itex] be the set of all functions [itex]f:\mathbf{N}\rightarrow\{0,1\}[/itex] that are eventually zero."

    But I don't really understand what is meant by that. Is it right to think about it as the set of binary numbers? If I take each [itex]f[/itex] to be a sequence of 0's and 1's and I read them from right to left then they are eventually zero right? I'm not sure this is the right way of thinking about this.
     
  2. jcsd
  3. Oct 5, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Marioqwe! :smile:
    yes

    an f:N -> {0,1} is a sequence of 0s and 1s

    for example, 110110100100000000000000…

    if it ends with all 0s after some time ("zero recurring"), then it is eventually zero :wink:
     
  4. Oct 5, 2012 #3
    Did you mean left to right? That's how to think of this. Another way to say it is that a binary sequence is eventually zero if it contains only finitely many 1's.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Set of functions that is eventually zero
  1. Functions and Sets? (Replies: 19)

Loading...