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I have found some pretty complete lists (I think) of mathematical symbols here and here, but I don't see a symbol for the word "and" on either list. A person could easily just write the word "and" or use an ampersand, but I was wondering if there was an actual mathematical symbol for the word "and". Also, if anyone knows any lists that are more complete than the ones I have linked to please provide a link.

Rócherz
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ubiquibacon
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3 Answers3

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The logical "and" is $\wedge$ (and the corresponding "or" is $\vee$).

Dirk
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    Let me note that, unless you are actually talking about formal logic (or set theory, etc.), most people never use this symbol to mean "and" in "ordinary" mathematics. It forces the reader to do more work to understand what you're saying, which is always bad, and it also has other meanings in mathematics. If you just want to use "and" in an ordinary sense like "a widget is a set satisfying P and Q," don't bother using this symbol. – Qiaochu Yuan Jan 24 '11 at 15:48
  • As a computer scientist, I am often confused by mathematicians' reluctance to use formal notation, favoring ambiguous natural language instead. (Not referring to your example, of course.) – Raphael Jan 24 '11 at 18:15
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    @Raphael: Formal notation (by which I mean dense notation filled with logical symbols like \forall and \exists) is hard to read. People are not computers. I'm not sure what you mean about ambiguity; can you give examples? – Qiaochu Yuan Jan 24 '11 at 19:42
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    Especially quantors are necessary sometimes: "Let $P(x,y)$ for all $x$ and some $y$." -- very typical. English "and" is commutative, but you may not exchange (different) quantors freely. So what you often find is really awkward semi-language in order to make things clear. If you are used to formula and they are well written (which can be hard) they are not at all hard to read. In fact, I have had more "What does he really mean?" moments than "What a crazy formula!" moments. Since this is obviously a matter of taste, good authors should provide both imho, i.e. idea + precise notion. – Raphael Jan 24 '11 at 21:30
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    And yes, in CS we tend to do things more formally because our consumers (computers, eventually) are dumb and can in most cases not disambiguate with context. But the same holds for non-peer readers. Things are naturally always clear to the author. – Raphael Jan 24 '11 at 21:33
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    Oh, another real example: "Let $R_x$ be the right flank of the left subtree, $L_x$ accordingly." Do I have to invert both directional adjectives or just one? – Raphael Jan 24 '11 at 21:34
  • @Raphael I am a computer scientist as well, hence the question. I am trying to develop a good "style" (for lack of a better term) for my mathematical notation. I am leaning towards using written words for all but the most common symbols. Math majors might know symbols like ∃ and ∈ when they see them, but most people would think they were looking at a funky eye chart. Writing the meaning of the symbol out doesn't take that much longer and seems to reduce confusion for everyone. – ubiquibacon Jan 24 '11 at 23:15
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    Well, as I said I do not think this is uniformly true. Personally, I think elaborating in proper natural language about your idea and the meaning of a statement and then put it there in its formal beauty. Having a crisp notation helps yourself and your reader, and by forcing yourself to write formally you also have to think very precisely, which is obviously a good thing. Natural language can often hide minor errors and abuses. You might be interested in this talk, too: http://modular.math.washington.edu/edu/basic/serre/ – Raphael Jan 24 '11 at 23:23
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    By the way, "they make me think harder" is rather an argument for than against formalism. A flashy sentence can often lull you into a false sense of understanding. – Raphael Jan 24 '11 at 23:25
  • Sometimes, $A\land B = \gcd(A,B)$ and $A\lor B=\text{lcm}(A,B)$. Thus, for and \ or, I commonly use $\barwedge$ and $\veebar$ respectively. Or, I put a dot inside $\land$ and $\lor$, depending on the circumstance, i.e. $\require{HTML} \style{display: inline-block; transform: rotate(90deg)}{\lessdot}$ and $\require{HTML} \style{display: inline-block; transform: rotate(90deg)}{\gtrdot}$. Ensure to state your kind of notation before you present it, though. – Mr Pie May 17 '18 at 00:39
  • @MrPie I think it's ok to use the same notation for both because one is defined on booleans and the other is defined on numbers. Moreover, it emphasizes the fact that both are meets in their respective contexts. – user76284 Oct 28 '19 at 18:24
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I'll also add that, perversely, the comma can mean either "and" or "or", depending on context. For example, in classical sequent calculus, $\{ P, Q \} \vdash \{ R, S \}$ means $P \land Q \vdash R \lor S$. Also, in set-builder notation $\{ \ldots : \ldots \}$, in a certain sense, commas in the left half are disjunctions and commas in the right half are conjunctions... which is the exact opposite of $\vdash$.

Zhen Lin
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The ampersand & is unmistakeable and just about right in semi-formal statements where "and" would be too wordy and a comma would be not very clear. The notation $\land$ is appropriate for formal logic, but isn't used much in general mathematics.

John Bentin
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