I'm looking for an adjective that means "to start from the number one."

This is so I can describe a sequence that starts from the number one. I want to be able to say something like "Choose any [adj] sequence" where [adj] is the adjective in this question.

I know there aren't always words that exist for every combination of words, but can anyone think of a word that might work for this?

  • At first I thought of a "positive" sequence of integers, but that doesn't necessarily start at 1. Do you mean in particular the sequences (1, 2, 3 ... n) where n is a positive integer? Or any old sequence that starts with 1? (In which latter case (1, -1, -3 ...) is valid.) – Adam Brown Jan 26 '14 at 2:19
  • I'm using the mathematical definition of a sequence so (1, 2, 3, ..., n) where n is a positive integer, (1, 3, 4), and (1, -2, -5) are all valid. – Patrick Jan 26 '14 at 3:14
  • In that case, I might say "starts with the number one" instead of "from the number one". – Adam Brown Jan 26 '14 at 4:53
  • Since the numbers in a sequence are all in an order, I think "starts from the number one" makes sense. – Patrick Jan 27 '14 at 5:50
  • Adam, out of curiosity, is there a name for the sequences (1, 2, 3, ..., n) where n is a positive integer? – Patrick Jan 27 '14 at 6:11

Given your clarification above, I don't believe that there is a single word to convey the property of beginning with 1 in such a general sense.

In a math context I would use "Choose any natural sequence having 1 as its first element" or "Choose any natural sequence that starts with 1."

Of course if this is a mathematics paper or assignment, it is perfectly acceptable to define a new term. Eg.: "Definition. A sequence of natural numbers is said to be one-grounded if it begins with 1." After which you can use the new term without fear of ambiguity.


A numbering or indexing system that starts from 1 is said to be one-based. By contrast, most of the widely used programming languages are zero-based.

See, for example, this article.

  • I think your suggestion is true for numbering or indexing systems but may not be understood/may have different connotations based on the context it's in which it's used and therefore doesn't mean starting from one in the general sense. For example, if I said "Choose any one-based sequence," it its only meaning "choose a sequence that starts from one"? Couldn't one take that to mean "choose any sequence that increments by one"? – Patrick Jan 26 '14 at 3:11
  • I think "one-based" would imply only sequences like (1, 2, 3, ... n). – Adam Brown Jan 26 '14 at 3:43
  • @AdamBrown To quote from the OP's question: "This is so I can describe a sequence that starts from the number one." – Gnawme Jan 26 '14 at 4:29
  • 1
    @Gnawme - Well, sure. (1, -10, 100, ...) is also a sequence that starts from one, but it strikes me as not suggested by "one-based". – Adam Brown Jan 26 '14 at 4:43

I would have thought "cardinal sequence" would work, but the mathematicians seem to have co-opted the term to mean something different.

  • Not sure I see your point. A cardinal number is defined as "any of the numbers that express amount" so a cardinal sequence would be "any of the sequences that express amount". Is there another definition of cardinal you're referring to? – Patrick Jan 27 '14 at 5:56
  • Cardinal as in a number used in counting. Wolfram says "In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, ....". – Spehro Pefhany Jan 27 '14 at 5:59

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