Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Lets say you have a sequence $S = (0, 1, 2, 3, 4, 5, 6, 7, 8)$

And another sequence $T = (0, 1, 2, 3)$

Is there any specific mathematical term that defines the relationship between $S$ and $T$, that specifically says that $S$ starts with $T$?

I thought $T$ would be called an initial sub-sequence, but this is incorrect because a sub-sequence seems to be a any subset of the elements of the sequence in the same order of the sequence (so even $(2, 4, 6, 8)$ would be a sub-sequence, while I want the prefix sub-sequence part, i.e. a sub-sequence that the sequence starts with)

share|improve this question

2 Answers 2

up vote 2 down vote accepted

I usually use "initial segment", and "tail segment" or "end segment" or "final segment" to denote the last part of a sequence.

If you want to indicate the segment is not everything, then "proper initial segment" should suffice.

share|improve this answer
    
Thanks, 'initial segment' fits more in what I am trying to express. –  jbx May 19 '13 at 14:26

In computer science (which is, at least at the beginning, maths), you call them words or strings over an alphabet $X$ which contains your letters.

For this alphabet $X$, you define $X^n$ by the usual Cartesian product and $X^*=\bigcup\limits_{n\in \Bbb N}X^n$. $X^*$ is the set of all words written with letters of $X$.

Then you can define a product $\cdot$ on $X^*$: $\left(u_1,\dots,u_p\right)\cdot \left(v_1,\dots,v_q\right)=\left(u_1,\dots,u_p,v_1,\dots,v_q\right)$

And so saying a word $u$ start with $v$ is saying : $\exists w \in X^*, u=v\cdot w$. And $v$ is therefore called a left factor of $u$, or a prefix.

share|improve this answer
    
Thanks for your answer. My context is actually computer science. I have a sequence of actions and I want to refer to the first few elements of the sequence. –  jbx May 18 '13 at 15:58
    
Well since you can also define the length of a word (the number of factors of $X^1$ needed to write the word), you can just say "the left factor/prefix of $v$ of length $k$"). –  xavierm02 May 18 '13 at 16:00

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.