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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


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    Hi Marioqwe! :smile:

    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.
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