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In the first post of the thread "Cardinal number subtraction",

Cardinal number subtraction

there is a symbol for some kind of set which looks like this: ℙ

I am familiar with symbols for natural ($\mathbb{N}$), rational ($\mathbb{Q}$), real ($\mathbb{R}$), complex ($\mathbb{C}$) numbers, which are all written in blackboard bold type. I am not a mathematician, but I have encountered all kinds of mathematical symbols, but not this one. I am very curious about this symbol. Does it stand for something?

Alex

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  • $\begingroup$ Thanks for the edit; now it looks better with blackboard bold type of letters. :-) $\endgroup$ – Aleksandar Katanovic Mar 29 '15 at 6:54
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I have seen $\mathbb{P}$ used for primes and for irrationals. I believe, from the context of the question you mention, that it was primes. I would not recommend using it without defining it as the notation is not as standard as the notation you mention.

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  • $\begingroup$ I agree - in the context of the linked question it should be primes $\endgroup$ – Peter Woolfitt Mar 29 '15 at 6:48
  • $\begingroup$ A sort of tangential remark, if my interpretation is correct they should have written $\mathbb{N} \setminus \mathbb{P}$ instead of $\mathbb{P} \setminus \mathbb{N}$. $\endgroup$ – Paul Plummer Mar 29 '15 at 6:59
  • $\begingroup$ Yep, that part confused me for a bit too $\endgroup$ – Peter Woolfitt Mar 29 '15 at 7:04
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It could mean anything. From a partial order to the set of primes, to a probability function.

In the context of that question, I'm guessing it meant the set of primes, and the observation that $|\Bbb{P\setminus N}|=\aleph_0$ was supposed to be $|\Bbb{N\setminus P}|$ instead.

But it doesn't matter for the context of the question $\Bbb P$ can be any countable infinite set which contains infinitely many elements which are not in $\Bbb N$.

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In the context of sets, if $X$ is a set the notation $\mathbb{P}(X)$ can be used to mean the power set of $X$. However, this is not universal notation, and the power set can also be referred to as $\mathcal{P}(X)$ or simply $P(X)$.

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  • $\begingroup$ In the post, it was written like this: Well, |ℙ|=ℵ0, and |ℙ∖ℕ|=ℵ0, so perhaps ℵ0−ℵ0=ℵ0? I am not sure if it can denote powerset, but perhaps the set of prime numbers, as it was mentioned by Disciple of Barney? $\endgroup$ – Aleksandar Katanovic Mar 29 '15 at 6:49
  • $\begingroup$ @AleksandarKatanovic Yeah, I looked at the post, and I agree with DiscipleofBarney's answer. $\endgroup$ – Peter Woolfitt Mar 29 '15 at 6:50
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    $\begingroup$ Script P stands for power sets but $\mathbb{P}(n)$ normally stands for the space of polynomials of order n $\endgroup$ – Triatticus Mar 29 '15 at 6:51
  • $\begingroup$ @AleksandarKatanovic (Though my answer is still valid for general use of the notation $\mathbb{P}$) $\endgroup$ – Peter Woolfitt Mar 29 '15 at 6:52
  • $\begingroup$ @Dan I think your statement would be reasonable as a separate answer if you wanted to post it. $\endgroup$ – Peter Woolfitt Mar 29 '15 at 6:53
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$\mathcal{P}(A)$ usually stands for the power set of a set A, meanwhile the set $\mathbb{P}(n)$ normally stands for the space of polynomials of order n

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