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Some conventional math notations seem arbitrary to English speakers but were mnemonic to non-English speakers who started them. To give a simple example, Z is the symbol for integers because of the German word Zahl(en) 'number(s)'. What are some more examples?

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i'm not sure if this is a relevant example, but this TED talk explains (more or less accurately, apparently) why $x$ prevailed for the unknown in equations ted.com/talks/terry_moore_why_is_x_the_unknown.html –  citedcorpse Aug 13 '13 at 13:23
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@MJD that claim is made in a footnote (typeset humorously in fraktur) in paolo aluffi's algebra book –  citedcorpse Aug 13 '13 at 13:47
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Why does $p$ stand for momentum? –  DepeHb Aug 13 '13 at 13:49
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a latin scholar will explain better, but the $p$ is from "impetus", a modified "petere" –  citedcorpse Aug 13 '13 at 13:52
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In topology the letter $F$ is commonly used to denote a closed set, from French fermé 'closed [set]'. The common use of $K$ to denote a compact set is probably from German kompakt, as in kompakte Menge 'compact set' and kompakter Raum 'compact space'. The common use of $k$ to denote an arbitrary field is probably from German Körper 'field'. The common use of $G$ for an open set is probably from German Gebiet 'region', though as a mathematical term it now means 'non-empty, connected, open set'. The notation $G_\delta$-set for the intersection of countably many open sets combines this $G$ with $\delta$ for German Durchschnitt 'intersection'. Presumably $F_\sigma$-set for the union of countably many closed sets is from the $F$ above and $\sigma$ for French somme 'sum'. The $T$ in the names of the separation axioms $T_1,T_2$, etc. is from German Trennungsaxiom 'separation axiom'.

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And in algebra $K$ is often used to denote a field from the German körper if I'm not mistaken. –  Stefan Hansen Aug 13 '13 at 13:12
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And $G$ as in $G_\delta$ sets is probably from the German "Gebiet" (domain). I've also heard the $\delta$ being short for "Durchsnitt". I've always found it funny that $F_\sigma$ and $G_\delta$ are from French and German respectively. –  mrf Aug 13 '13 at 13:28
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@MTurgeon: Very unlikely: one speaks of eine offene Menge, not eine geöffnete Menge. –  Brian M. Scott Aug 13 '13 at 13:41
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@SamiBenRomdhane: I suspect that most English speakers who use $O$ for an open set do so on account of open and aren't even aware of ouvert. (I prefer not to use $O$ at all, for anything, owing to its resemblance to $0$.) –  Brian M. Scott Aug 13 '13 at 13:43
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The use of $U$ for open sets probably comes from the German Umgebung "neighbourhood". –  Miha Habič Aug 13 '13 at 14:53
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Eigen (as in the eigen vectors of a matrix) is Dutch/German for "own".

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+ for mentioning Dutch ;) –  Michal B. Aug 14 '13 at 12:32
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A function is often called càdlàg if it is right-continuous and admits left limits. This term is from the french continue à droite, limite à gauche.

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See also càglàd (obvious) and càllàl (continue à l'une, limite à l'autre, meaning continuous on one side, limit on the other side, and which side is continuous can depend on the point). –  jwg Aug 13 '13 at 14:49
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$\ln()$ for "logarithmus naturalis"?

My advisor also told me that the "socle of a ring" makes a little more sense when you know that "socle" is an architecture term for the support underneath a column or pedastal, and so the socle of a ring acts as a kind of "support for the ring." In some languages, the word for "pedestal" is something like "socle," so the meaning is less hidden there.

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When I put "socle" into google translate, it autodetects it as "plinth" which is a relatively better-known word in English. It turns into "zócalo" in Spanish, sòcol in Catalan, Sockel in German, zoccolo in Italian, cokół in Polish, soco in Romanian, and 虹晶 in Mandarin.

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I always wondered what socle was supposed to mean! –  Matt Pressland Aug 13 '13 at 13:11
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Not quite true: socle has that meaning in architecture, but the Latin base is actually socculus, a diminutive of soccus 'a slipper, a sock'. –  Brian M. Scott Aug 13 '13 at 13:16
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the Dutch "sokkel" means pedestal –  ratchet freak Aug 13 '13 at 15:59
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I made changes to pacify those with a deep knowledge of Latin roots. Apparently Latin roots are completely useless for understanding words if you go back far enough. –  rschwieb Aug 13 '13 at 19:50
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@JyrkiLahtonen Yeah it does mean that in English, but English speakers hardly ever use it unless they know about architecture. –  rschwieb Aug 14 '13 at 19:28
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The Klein $V$-group is the four-element group with generators $a$ and $b$ and $a^2 = b^2 = (ab)^2 = 1$. The $V$ is for vierergruppe = "four-group".

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Łukasiewicz notation for logic represents $\land \lor \leftrightarrow$ with the letters $K A E$ respectively, so that for example $r\lor(p\land q)$ is $ArKpq$. $K A E$ are the initials of the Polish words koniunkcja, alternatywa, ekwiwalencja.

I don't know why Łukasiewicz used $C$ to represent material implication.

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$p \implies q$ ------ $p$ czyli $q$ –  DepeHb Aug 13 '13 at 13:53
    
Are you sure this is the reason? I am not a Polish speaker, but the examples I have found of czyli do not seem very much like material implication. –  MJD Aug 13 '13 at 15:09
    
It's synonymous with 'therefore' and definitely can be used in this context. Whether this was his reason for $C$ I can't say, but it certainly is a (perhaps somewhat archaic) way of expressing implication. –  DepeHb Aug 13 '13 at 15:58
    
I am a Polish speaker, and it certainly seems reasonable. Here's a link to the relevant Wiktionary article: en.wiktionary.org/wiki/czyli –  Matthew Piziak Aug 13 '13 at 18:21
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I had read that when I posted my comment above. I also consulted with Maciej Cegłowski, who though not a linguist is a native Polish speaker, and who agreed with me that it seems unlikely. My own suspicion is that $C$ is short for "conditional". –  MJD Aug 14 '13 at 19:08
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The reason the "Klein bottle" is called a bottle has its origin in something of a German pun on Fläche/Flasche; see here

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this is also why when one wants to talk about two surfaces, one uses $S$ and $F$ –  citedcorpse Aug 13 '13 at 13:48
    
Similarly, the Witch of Agnesi takes its English name from a pun in Italian, at least according to Wikipedia. –  Hammerite Aug 14 '13 at 1:39
    
These answers should be posted as a separate answers to give them proper visibility. Not everybody is aware of these facts. –  user72694 Aug 14 '13 at 7:39
    
Well, I thought about it, but it isn't really a piece of notation or a mnemonic as such, more an interesting tidbit (although I don't want to imply disapproval of your choice to post yours as an answer). –  Hammerite Aug 14 '13 at 21:49
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Gabriel introduced the notation $\text{Sex}(\mathcal A,\mathcal B)$ to denote the category of left exact functors from $\mathcal A$ to $\mathcal B$. This because the Latin word for left (which is sinister) starts with an S.

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Is the category of right exact functors called $\text{Dex}(\mathcal A,\mathcal B)$ from dexter? –  Matthew Piziak Aug 13 '13 at 18:42
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In homology one has a sequence of "differentials". Their images are usually denoted $B(X)$, apparently from the german word for "images", and their kernels $Z(X)$ from the german word for "cycles".

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I always thought $B$ stood for "boundary". –  Zhen Lin Aug 13 '13 at 13:20
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@ZhenLin i think that's more of an ad-hoc thing that we do when working in english, to try to make more sense of it. one could then say we use $Z$ to stand for "zeroes", which is actually kind of pleasant –  citedcorpse Aug 13 '13 at 13:22
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The etymology of the $\sin$ function has a colorful history - it comes from sinus, the latin word for... well, bosom. This was due to a mistranslation from Arabic text in the 12th century: The word jaib means bosom, and since Arabic is written without short vowels, it was written essentially as jb. But jb was also the spelling of jiba, which was a transliteration of the Sanskrit word for chord (the mathematical chord, ie a line passing through a circle, half the length of which is the sine of the angle from the center of the cicle).

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According to my Latin dictionary, sinus also means "curve". Which might be a simpler explanation than the mistranslation one. –  detly Aug 13 '13 at 22:07
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@detly but much less funny –  ratchet freak Aug 14 '13 at 11:25
    
All those meanings are present in Spanish: "seno = concavity, bosom, and trig $\sin$" –  leonbloy Aug 16 '13 at 13:54
    
And I doubt it's a mistranslation, the relation of meanings ("curved things") is apparent. See also this figure: 1.bp.blogspot.com/-DniqyzYnS0Y/Tf5Xx7mpoLI/AAAAAAAAANo/… –  leonbloy Aug 16 '13 at 14:02
    
Interesting, I wasn't aware of this. I'd be interested to see if there's more reasoning behind scholars believing that this was a mistranslation, but I don't have access to the sources in the wikipedia article: en.wikipedia.org/wiki/Sine#Etymology –  MartianInvader Aug 16 '13 at 15:40
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The logical-or symbol $\lor$ is a stylized letter ‘V’, the first letter of the Latin word vel.

(The $\land$ symbol arose later, derived by analogy from $\lor$.)

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I always remember "and" because it looks like an "A". And "or" because it's an upside-down "and". –  Joe Z. Aug 13 '13 at 17:09
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QED comes from the latin quod erat demonstrandum

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In french, it's CQFD for "ce qu'il faut démontrer" == "Which had to be demonstrated". Just for your curiosity. –  Fabinout Aug 14 '13 at 8:03
    
@Fabinout Being french, I know that, although I'd say "Ce qu'il fallait démontrer". ;) –  Jean-Sébastien Aug 14 '13 at 14:31
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In Polya's enumeration theorem the letter $Z(G)$ which is used for the cycle index of the permutation group $G$ originates with the German word Zyklenzeiger, I think.

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The center of a group $G$ is denoted $Z(G)$. The $Z$ is for “Zentrum”, which is the German word for ‘center’.

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