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I'm reading a paper that refers to a set $\mathcal{N}$, without defining it. It's a CS paper so it's not complicated maths. Is this the set of natural numbers? I don't get why they're using this style of N over a blackboard N.


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closed as off topic by Andreas Thom, Martin Brandenburg, Felipe Voloch, Mark Sapir, Gerald Edgar Jul 20 '11 at 12:44

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(a) I retagged, since it is actually not about set-theory. (b) You'd do better if you actual link to the paper, or if you quote a selection of the text where the notation is used. For things that are undefined, context is what enables us to figure out what they mean. – Willie Wong Jul 20 '11 at 11:49
Probably you should ask in a CS forum. – Gerald Edgar Jul 20 '11 at 12:28
It can be used to denote the natural numbers in CS, as in the paper linked in this MO answer:… – Mark Grant Jul 20 '11 at 12:34
Interesting that this is about to be closed while the now doubly linked question was received so well. – quid Jul 20 '11 at 12:40

In 'PRIMES is in P' (for example), yes these are the natural numbers.

There are various authors that do not use $\mathbb{N}$, and more generally do not use blackboard bold at all in print. As I mentioned on a recent question Jean-Pierre Serre is on record against balckboard bold (except on black boards). Though, a more typical choice then is $\mathbf{N}$, so standard bold. I could imagine that in CS, in particular when complexity classes are around, one wishes to have more optical distance between capital letters denoting complexity classes and those denoting sets. But this is mainly a guess.

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