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This is for math. In Latex, you get these symbols with \mathbb{}. They are most commonly used to represent to represent number sets, like the set of all intege
by dietrichepp 3y ago
This is for math.
In Latex, you get these symbols with \mathbb{}. They are most commonly used to represent to represent number sets, like the set of all integers Z (from the German), set of all natural numbers N, set of complex numbers C, set of all real numbers R, rationals Q (for “quotient”), set of quaternions H (named after Hamilton), or an unknown set F (for “field”). This explains why many of the letters in this series exist in the basic multilingual plane—because R is very commonly used, but A is not. You can find ℝ in the basic multilingual plane at U+211D.
I don’t know why people are interested in the X symbol. It’s just there to complete the alphabet. There are many other ranges like this used for writing mathematical formulas, like the range of bold letters, fraktur, script, etc.
- orlp 3y ago𝕏 is used as a symbol for a generic metric space. E.g. if your result is generic over ℝ², ℂ³, etc, you can write 𝕏.
- dietrichepp 3y agoThanks! I am always a little curious about how these symbols are used. That makes perfect sense to me.
- red_trumpet 3y agoI'm a PhD student in algebraic geometry and have seldom seen this. IME "X" is a generic name for all kinds of spaces (metric, topological, complex analytic, algebraic...), but I don't remember ever having seen "𝕏". That said, in principal everyone is free to call their spaces how they like. It just makes it easier to read if one sticks to familiar notation.
- orlp 3y agoYou'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.
- tmccrary55 3y ago[flagged]
- throw0101b 3y ago> Because Elmo Please do not sully the good name of the Muppet by associating him with the tech billionaire…
- krger 3y agoElmo (and specifically the value-extraction-by-merchandise craze CTW created around him) pretty much single-handedly destroyed the original ensemble cast spirit of Sesame Street, so it's actually pretty apt.
- masukomi 3y agobecause elon renamed twitter to "x corp", bought the x.com domain and shoved this character on it.
- mkl 3y agoHe (or a company of his) has had the x.com domain for decades: https://en.wikipedia.org/wiki/X.com https://en.wikipedia.org/wiki/X.com
- spread_love 3y agoNo, it changed ownership many times since 1999. > On July 5 2017, Musk repurchased the domain name X.com from PayPal They even took a little jab at him when it happened > "We are delighted to sell the domain x.com back to its previous owner"
- pilsetnieks 3y ago[flagged]
- deadbunny 3y ago> On July 5 2017 2017 is not 1999
- gilleain 3y agoGiven the start of this thread was about N, C, X etc ... We could even say "2017 > 1999", giving an ordering over these numbers.
- mkl 3y agoI think you missed the point: the domain has not been in Musk's control that whole time, as I had thought. His company X.com had it, then PayPal got it when it was created in the merger of X.com and Confinity, and PayPal kept it after Musk left, but then Musk got it back.
- dclowd9901 3y agoCause “X” is a cool letter. Just ask David X. Cohen.
- jhoechtl 3y ago> I don’t know why people are interested in the X symbol. It's the new symbol for and domain name of the social? network formerly known as twitter.
- plagiarist 3y ago[flagged]
- dang 3y agoCan you please not break the site guidelines by fulminating, name-calling, snarking, and so on? It's not what this site is for, and destroys what it is for. You may not owe $CEO better, but you owe this community better if you're participating in it. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- astrange 3y agoNot to mention the X.org logo.
- formerly_proven 3y agoThe "bb" in "mathbb" isn't for "math, baby" (although accurate), but short for "blackboard bold". These letterforms don't originate with blackboards though, using outlines for thick verticals goes back centuries. They're sometimes called open face.
- enriquto 3y ago> This is for math. Heh. The "tabs vs spaces" debate of mathematical typography is whether these symbols should be used at all in printing, or reserved for actual blackboards. In LaTeX you can have actual boldface letters, so you should write a boldface letter R to represent the real numbers and so on. Using "blackboard bold" in print looks terribly off to some (many?) people.
- folkrav 3y agoFunny. Coming from a non-math background, having only one symbol to deal with feels less confusing than switching around symbols based on the medium it happens to be written on. Did one of the symbols come "first"?
- enriquto 3y agoHere you have the whole history: https://en.wikipedia.org/wiki/Blackboard_bold https://en.wikipedia.org/wiki/Blackboard_bold Summary: boldface came first, in print, and was widely used. Much later, some mathematicians started to write blackboard bold on blackboards (because actual bold would be very untoward to write on a blackboard). Then, the usage was backported to print. I find it ugly, a sort of breaking "suspension of disbelief", I don't know how to explain why. Some sort of "anachronistic" feeling, like watching a movie about the roman empire and some soldiers wear watches. EDIT: as for having "different symbols", this is not the case. They are exactly the same symbol, with different faces. Like when you write the letters "a" or "g" very different on a blackboard as they appear on print.
- dietrichepp 3y agoIt sounds similar to the division between “math” and “maths”. It looks wrong depending on where you grew up.
- dataflow 3y agoWe can compromise by switching to mathematic.
- snarfy 3y agoThey are an accessibility nightmare. I read a comment here recently from a blind person that had to give up on math education entirely due to all of the symbols not being supported by screen readers. It was pretty sad.
- thebooktocome 3y agoOne blind mathematician I know prefers reading LaTeX over pdf math for exactly this reason.
- blincoln 3y agoI avoid using oddball Unicode characters for this reason,[1] but I also feel like at this point the can of worms has been unleashed, and the screen reader authors are going to have to adapt to a more hostile environment. It seems like one approach might be something like this, assuming none of them are doing it already. If this is TLDR, the key feature relating to the topic at hand is the point about handling mathematical symbols, so skip everything except that one. * Pre-parse the entire page and count the number of characters that would be read using a multi-word description. While doing this, create sub-counts of characters that fall into each Unicode script (Latin, Cyrillic, mathematical notation, etc.). * If the number of characters that would be read using a multi-word description exceeds a user-specified threshold, prompt the user for how to proceed. * First, tell the user how many different Unicode scripts (and blocks if necessary[2]) are contained on the page. For each set, prompt using the following logic if the user hasn't already set a default: ** If a script/block/whatever consists of abstract symbols, like the mathematical set, offer to read it using the closest approximation in the character set it's derived from. e.g. for 𝕏, read it as "X" instead of "mathematical double-struck capital X". Read both 𝜸 ℾ as "gamma" instead of their lengthy "mathematical..." descriptions. ** If a script/block/whatever represents a spoken language, offer to do one of the following: ** Read it as if spoken by someone fluent in the language. ** Precede it with "the following [n] [script name] characters" and read each one individually, without any leading per-letter indicators, e.g. for "ΑΒΓΔ", "the following four Greek characters: alpha, beta, gamma, delta". Optionally include per-letter capitalization indication, but only if the user has previous enabled that option. ** Replace it with a count and the script name, e.g. "five hundred characters of Chinese script". Provide a way for the user to interrupt the narration and expand that section instead of omitting it. * Allow the user to store all of the prompt answers as defaults and not prompt them again unless the user resets the option. e.g. "always read mathematical symbols as the closest Latin letter approximation". * Maybe remind the user that it is an option in edge cases like "this entire page would be read as 'a series of 53,198 symbols you've suppressed reading'". [1] One of my first full-time jobs, decades ago, was doing UI development with a focus on accessibility. [2] Pretty unbelievable that the Unicode consortium has taken the position that an apparently unlimited number of stylistic variations on Latin letters should get their own Unicode renditions, but that basically every other culture's character sets gets merged into one style of character even if there are extensive historical reasons to have different renderings, and also has the time to keep adding corner-case emojis, but can't be bothered to provide a single way to easily differentiate "Cyrillic" from "Latin" as well as differentiate "mathematical notation" from "Latin".
- deleted 3y ago[deleted]
- eesmith 3y agoOoh, I found a use in the wild! https://www.ams.org/books/memo/1023/ https://www.ams.org/books/memo/1023/ The central theme of this paper is the variational analysis of homeomorphisms $h \colon \mathbb X \xrightarrow []{{}_{\!\!\mathrm {onto}\!\!}}\mathbb Y$ between two given domains $\mathbb X , \mathbb Y \subset \mathbb R^n$.