# What word am I looking for (similar to “subset”)

If...

• (A) is a subset of (A)
• (A,B) is a subset of (A,B,C)
• (B,A) is not a subset of (A,B,C) because order matters.
• (B,C) is not a subset of (A,B,C) because I only want to compare the front of each set.

Now subset is the second cousin of the word I'm actually looking for. Which word would best fit here?

Maybe:

• is a prefix of
• begins

... but they seem awkward. Bonus points if there's a common term with an accepted Mathematical meaning (I'm not sure if some term exists).

• Looks like you're not looking at sets or ordered tuples, but at subsequences of the string ABC..., which all begin with the first element of that string? – Wayfaring Stranger Oct 24 '13 at 18:28
• Subsequence! That's much much closer to what I'm getting at. – Michael J Swart Oct 24 '13 at 18:30
• Prefix is the standard term for this, not awkward one little bit. – n.m. Oct 24 '13 at 18:31
• Subsequence is the standard term for another concept. See here for more info. – n.m. Oct 24 '13 at 18:38
• It is not unusual at all to talk about prefixes of sequences. In fact a string is just a finite sequence of elements drawn from a finite set, called the alphabet. {apple, orange, pear} is a perfectly good alphabet as far as mathematics is concerned. – n.m. Oct 24 '13 at 19:41

This looks like a branch of Math called Formal Language Theory. The terminology of Formal Language Theory generally comes from everyday English, and terms like prefixes, is a prefix of, begins (with) and starts (with) are commonly used.

It might be called initial segment.

References here and here.

It's not a single word, but what about "ordered initial subset" or "initial subsequence"?

You might try preamble or truncated form.

(A,B) is a preamble to (A,B,C,D)

(A,B) is a truncated form of (A,B,C,D)