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Suppose I have a set of numbers. Then, suppose further that I take a sample of this set. Which of my sentences is correct? and why?

Let (0,2) be a sample from a set S of discrete numbers

or

Let (0,2) be a sample from set S of discrete numbers

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    If you're trying to use formal mathematical language, then subset might be a better choice than sample. Also, curly braces {} are customary for (sub)sets rather than parentheses (), which are more commonly used for vectors or coordinates. – Canadian Yankee Jan 10 at 13:25
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The first is correct. When you are first introducing an unknown object in a discussion (in this case, some arbitrary set S of discrete numbers) you have to precede the noun with the indefinite article 'a' or 'an'. Using the indefinite article is not optional in English, in this case.

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Another way you could say that is:

Let (0,2) be a sample from a set of discrete numbers, S.

or

Given a set of discrete numbers, S, let (0,2) be a sample from S.

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