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Logic Notation

(for example) I want to write a≠b∧b≠c∧c≠aa \not= b \land b \not= c \land c \not= a

Is there a way to write this using nice fancy notation similar to this

:

Its just much nicer than ai≠aj ∀ai,aj∈a_i \not= a_j\ \forall a_i,a_j \in{a,b,c}∧i≠j \land i \not= jThanks
(edited 8 years ago)
Reply 1
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Zacken
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Original post by Johann von Gauss
I want to write a≠b∧b≠c∧c≠aa \not= b \land b \not= c \land c \not= a

Is there a way to write this using nice fancy notation similar to this:



Its just much nicer than ai≠aj ∀ai,aj∈a_i \not= a_j\ \forall a_i,a_j \in{a,b,c}∧i≠j \land i \not= j

Thanks :smile:


http://tex.stackexchange.com/questions/64989/how-to-type-big-and-symbol
Can you not just say, a,b,c are distinct values, or whatever they are.
Reply 3
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Zacken
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Original post by ghostwalker
Can you not just say, a,b,c are distinct values, or whatever they are.


Precisely what I'd do as well - I'd take some English over obscure logic notation if it isn't necessary anyday.
Original post by Zacken


Thanks, do you happen to know what the 'big and' symbol is called? I've never seen it anywhere (except your link), but I can't see any reason it wouldn't be used. That's the only result on Google for "big and" logic symbol - not sure what to search tbh.

Original post by Zacken
Precisely what I'd do as well - I'd take some English over obscure logic notation if it isn't necessary anyday.

A sentence in maths feels like an essay to me... painful to write words when I'm itching to do maths

Original post by ghostwalker
Can you not just say, a,b,c are distinct values, or whatever they are.
Yes, but I'm asking if I can use this nicer notation (or similar)?
(edited 8 years ago)
Reply 5
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Zacken
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Original post by Johann von Gauss
Thanks, do you happen to know what the 'big and' symbol is called? I've never seen it anywhere (except your link), but I can't see any reason it wouldn't be used


A sentence in maths feels like an essay to me... painful to write words when I'm itching to do maths


To each his own, I suppose. :lol:

I don't think there is a name for it - is there name for the big union operator?
\bigwedge if you want the LaTex. And \bigvee for the "or" equivalent.
Like this? Is this an acceptable way to represent "a,b,c are distinct"?

⋀cyc(abc)(a≠b)\bigwedge_{cyc(a b c)} (a \not= b)
Original post by Johann von Gauss
Like this? Is this an acceptable way to represent "a,b,c are distinct"?

⋀cyc(abc)(a≠b)\bigwedge_{cyc(a b c)} (a \not= b)


Not something I've every seen.

Not familiar with the \cyc as some form of indexing, or at all.

And it doesn't look right to have a,b in both the set you're selecting from and as the terms in the conjunction.

What are a,b,c?
Original post by ghostwalker
Not something I've every seen.

Not familiar with the \cyc as some form of indexing, or at all.

And it doesn't look right to have a,b in both the set you're selecting from and as the terms in the conjunction.

What are a,b,c?


AFAIK, cyc(abc) is more informal notation for a cyclic permutation (a to b to c to a), i.e. ∑cyc(abc)f(a,b,c)=f(a,b,c)+f(b,c,a)+f(c,a,b)\sum_{cyc(abc)}f(a,b,c) = f(a,b,c)+f(b,c,a)+f(c,a,b)
Original post by Johann von Gauss
AFAIK, cyc(abc) is more informal notation for a cyclic permutation (a to b to c to a), i.e. ∑cyc(abc)f(a,b,c)=f(a,b,c)+f(b,c,a)+f(c,a,b)\sum_{cyc(abc)}f(a,b,c) = f(a,b,c)+f(b,c,a)+f(c,a,b)


In that case it seems reasonable.
Original post by Johann von Gauss
Like this? Is this an acceptable way to represent "a,b,c are distinct"?

⋀cyc(abc)(a≠b)\bigwedge_{cyc(a b c)} (a \not= b)


Only if it's acceptable to make your intention incomprehensible. All IMHO, of course.
Original post by atsruser
Only if it's acceptable to make your intention incomprehensible. All IMHO, of course.


Is it not used much at higher levels? I'd assumed more advanced maths would use these kinds of symbols. I'm only an A-level student.

Original post by ghostwalker
In that case it seems reasonable.


People on this site use cyc notation a lot:

http://www.artofproblemsolving.com/community/c6h1160744_inequality
Original post by Johann von Gauss
Is it not used much at higher levels? I'd assumed more advanced maths would use these kinds of symbols. I'm only an A-level student.


It may be used in formal logic, but I've not seen it used in "normal" mathematics. I ought to add that I fall into the "use English" camp though; I don't even like ∃,∀\exists, \forall much though.




Maybe it's useful in number theory type problems as well. I don't think I could follow an argument which used it too well without writing it all out in full. Maybe I'd get used to it with practise.
Original post by atsruser
Maybe it's useful in number theory type problems as well. I don't think I could follow an argument which used it too well without writing it all out in full. Maybe I'd get used to it with practise.
It comes up a lot in inequalities questions (BMO/IMO type stuff). You also sometimes see it used in discussion about roots of polynomials, symmetric polys and stuff like that.

I'd say it's definitely not mainstream though. It's at the level where a fairly well read mathmo would probably have seen it used, but would be unlikely to have used it themselves.

It's probably no surprise to those who've seen some of my rants about notation that I agree with the people saying "what's wrong with using English?", however...

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