# Set of functions that is eventually zero

1. Oct 5, 2012

### Marioqwe

Usually, in homework problems, I come across something like, "Let $F$ be the set of all functions $f:\mathbf{N}\rightarrow\{0,1\}$ 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 $f$ 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. Oct 5, 2012

### tiny-tim

Hi Marioqwe!
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

3. Oct 5, 2012

### SteveL27

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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