"Greater than" or "Greater than or equal" Below is a question I encountered:
Question
My answer was $\{x \mid x \in Z, -1 \leq x \leq 4 \}$
However, the textbook answer stated $\{x \mid x \in Z, -1 \leq x < 5\}$
Can $\leq$ and $<$ be used interchangeably in this situation?
Is there a more accepted convention?
Thanks,
George
 A: I don't think that there's a convention about if you should use $\leq$ or $<$, but I do think that whichever you do you should be consistent. Writing $-1\leq x<5$ like the book has can very easily lead to confusion because people will miss the fact that the "or equal" was dropped. In fact, when I read this at first I went "Ah ha! The book has a typo, it should say $-2<x<5$."
A: If we take you literally, the answer to your question "Can $\leq$ and $<$ be used interchangeably in this situation?" is no: $\leq$ and $<$ cannot "be used interchangeably." For the statement $x\leq 4$ is not equivalent to the statement $x<4$. You can't interchange $\leq$ with $<$ without changing something else in the statement.
But perhaps you didn't write what you meant to ask. Perhaps you meant: is there a reason to prefer the notation $x\leq 4$ to the notation $x<5$ when $x$ denotes an integer? In that case, the answer to your question is still no: it's just a convention; both inequalities refer to the same set of integers.
