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section 1.1 of the book "Introduction to Probability, 2nd Edition" says

If S is a set and x is an element of S, we write x ∈ S.

If S contains a finite number of elements, say X1, X2, ...

similar usage of “say” shows up everywhere.

Is "say" a simplified version of "let's say" here?

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    Say is used here to mean for example. Let's say also works. – Davo Jul 30 '19 at 13:14
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In this case SAY indicates that the following text is information given to you to allow you to solve your mathematical problem.

say verb (GIVE INFORMATION) to provide information or instructions in writing: Link C.E.D.

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