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.
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4$\begingroup$ Actually "and" is in the second link you gave us under "logical conjunction". $\endgroup$– ListingCommented Jan 24, 2011 at 15:26
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2$\begingroup$ @user3123 haha, so it is. Thanks for pointing that out! $\endgroup$– ubiquibaconCommented Jan 24, 2011 at 15:43
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$\begingroup$ Please check the notation tag wiki for a link. $\endgroup$– AryabhataCommented Jan 24, 2011 at 17:10
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$\begingroup$ It's also not uncommon to write something like "a<b,c" to indicate that "a<b and a<c". In my opinion, you should mostly write what's easiest for the reader to extract the meaning from. $\endgroup$– MyselfCommented Jan 24, 2011 at 18:54
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3 Answers
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The logical "and" is $\wedge$ (and the corresponding "or" is $\vee$).
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11$\begingroup$ 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. $\endgroup$ Commented Jan 24, 2011 at 15:48
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3$\begingroup$ @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? $\endgroup$ Commented Jan 24, 2011 at 19:42
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3$\begingroup$ 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. $\endgroup$– RaphaelCommented Jan 24, 2011 at 21:30
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2$\begingroup$ 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. $\endgroup$– RaphaelCommented Jan 24, 2011 at 21:33
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1$\begingroup$ 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? $\endgroup$– RaphaelCommented Jan 24, 2011 at 21:34
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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 $\vdash$.
answered Jan 24, 2011 at 16:16
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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.
answered Jan 24, 2011 at 18:52