# Proper notation to represent a set containing sequences of numbers for scientific papers?

I would like to include a set of numbers, which are composed of by multiple sequences, for example:

{1,2,3,4,5, at steps of 1 ... till 100, 200, 500, then 1000, 2000, at steps of 1000 .... till 10000}

Is there a proper way to represent this? I tried looking up some scheduling papers in OR/IEEE journals but have yet to find papers that include such notation explicitly.

• One tiny detail: in the title, you write "sequence of numbers", in the text, you write "set of numbers". The term "sequence" typically refers to an ordered set. If you need to retain the order in your work, a set-based notation is not quite what you need. If you actually mean "set", then you may want to change the title of your post. Feb 27 '15 at 9:43
• "Positive integers from 1 to 100, the exceptional values 200 and 500, and positive multiples of 1000 up to 10000" Feb 27 '15 at 15:48
• The way you explained the sequence in your question seems fine to me. Feb 28 '15 at 0:05

I'd recommend standard mathematical notation, which should be sufficiently unambiguous yet legible. Use the standard "union" symbol (\cup in LaTeX) to denote separate sets you want to take the union over.

Unfortunately, no MathJax here - so here is the LaTeX code and below the result (done using CodeCogs):

\{k\in\mathbb{N}\mid 1\leq k\leq 100\}
\cup \{200,500\}
\cup\{1000k\mid k\in\mathbb{N}, 1\leq k\leq 10\} Depending on your layout (one vs. two columns), insert linebreaks at appropriate places, e.g., like I did in the LaTeX code but not the result.

• I think it depends on your field. If you were to put that in a mechanical engineering journal it would at least be thought a bit odd. Feb 27 '15 at 9:59