In common academic practice (i.e. formal mathematics papers, books, research, etc.), you use
to denote the natural numbers,
to denote the integers,
to denote the rational numbers,
to denote the real numbers, and
to denote the complex numbers. Occasionally you might see
instead, but this isn't particularly common (though I've seen people like Terry Tao use it all the time, so it's certainly not unheard of). However, I've never seen
used to mean the same thing. In general the caligraphic style
isn't used to describe such subsets of the complex numbers.
As the irrationals are much less important than these sets, they usually are just written
, although I have seen them written as both
and
.
All that being said, I seem to remember using the notation
to denote the integers in spec exams back in the day, so maybe that's the standard in spec. Check your textbook perhaps? Whatever they use there will definitely be accepted by examiners.
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