What does $P$ in blackboard bold type of letter stand for? $\Bbb P$?

Question

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

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

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

Thanks for the edit; now it looks better with blackboard bold type of letters. :-) — Aleksandar Katanovic, Mar 29 '15 at 06:54

score 5 · Answer 1 · 2015-03-29T06:46:57.473

5

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.

edited Mar 29 '15 at 06:46

answered Mar 29 '15 at 06:41

I agree - in the context of the linked question it should be primes – Peter Woolfitt Mar 29 '15 at 06:48
A sort of tangential remark, if my interpretation is correct they should have written $\mathbb{N} \setminus \mathbb{P}$ instead of $\mathbb{P} \setminus \mathbb{N}$. – Mar 29 '15 at 06:59
Yep, that part confused me for a bit too – Peter Woolfitt Mar 29 '15 at 07:04

score 1 · Answer 2 · answered Mar 29 '15 at 08:11

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 $\Bbb N$.

score 0 · Answer 3 · answered Mar 29 '15 at 06:39

0

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 $P(X)$.

answered Mar 29 '15 at 06:39

Peter Woolfitt

21,114

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?
– Aleksandar Katanovic Mar 29 '15 at 06:49
@AleksandarKatanovic Yeah, I looked at the post, and I agree with DiscipleofBarney's answer. – Peter Woolfitt Mar 29 '15 at 06:50
1

Script P stands for power sets but $\mathbb{P}(n)$ normally stands for the space of polynomials of order n – Triatticus Mar 29 '15 at 06:51
@AleksandarKatanovic (Though my answer is still valid for general use of the notation $\mathbb{P}$) – Peter Woolfitt Mar 29 '15 at 06:52
@Dan I think your statement would be reasonable as a separate answer if you wanted to post it. – Peter Woolfitt Mar 29 '15 at 06:53
Thanks Peter Woolfitt, usually this is how I interpret linear algebra – Triatticus Mar 29 '15 at 07:02

score 0 · Answer 4 · answered Mar 29 '15 at 06:57

0

$\mathcal{P}(A)$ 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

answered Mar 29 '15 at 06:57

Triatticus

1,232

What does $P$ in blackboard bold type of letter stand for? $\Bbb P$?

4 Answers4

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