4 ms·
You're right I should've used "as a symbol" not "as the symbol". It's not terribly common.
by orlp 3y ago
You're right I should've used "as a symbol" not "as the symbol". It's not terribly common.
- red_trumpet 3y agoNow that I think about it, most double stroked characters really represent "concrete" objects, not generic ones. Like ℙ for projective space, or 𝔸 for affine space. Also 𝔽 is often used together with an index 𝔽_q for the field with q elements. On the other hand, Wikipedia[1] agrees with you, that 𝕏 is "occasionally" used for metric spaces. [1] https://en.wikipedia.org/wiki/Blackboard_bold https://en.wikipedia.org/wiki/Blackboard_bold
- dietrichepp 3y agoMy experience with 𝔽 is “vector space over a field 𝔽”, which is not a concrete object, but I have probably seen F written in a normal italic style more often.
- orlp 3y agoAs a counterpoint, 𝔽 when not fixed to a particular size is arguably still generic over "any field", and 𝔾 is most definitely generic for "any group", even if fixed to a particular size.
- red_trumpet 3y agoThere might be small cultural differences at hand here. As a German, I prefer "k" or "K" for fields (as in "Körper"), and I think I've seen 𝔾 mostly as 𝔾_a or 𝔾_m for the additive and multiplicative group. shrug
- dataflow 3y agoI've seen ℙ used for probability.
- runarberg 3y agoI’ve also seen ⅆ as the differential operator and 𝔼(X) as the expected value of X. I think I’ve also seen 𝟙_x, and ⅈ, and ⅉ but I don’t remember for what.
- brewmarche 3y agoI know 𝟙_X as the indicator function (also called characteristic function) of X in measure theory and probability theory, but I’ve also seen 1_X or χ_X. ⅈ and ⅉ can be basis vectors or imaginary units although I’ve never seen them in blackboard bold in my lectures.
- ginnungagap 3y agoIn set theory blackboard bold P, Q and C are very often used for arbitrary (forcing) posets
- nephanth 3y agoI've seen (and used) \mathbb{P} and \mathbb{E} for the probability & expectation operators (so not really a "concrete" object in your sense?)