ParadigmShifter
Random Nonsense Generator
Pfft, Physics. Far too useful.
Ask a Mathematician!
- Thread starter IdiotsOpposite
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IdiotsOpposite
Boom, headshot.
They have a dedicated math section too! We once had a wonderful and enlightening debate on why the Riemann Hypothesis is or isn't true. I was on the "is" side, of course.
ParadigmShifter
Random Nonsense Generator
Of course? That's not the mathematical way of thinking. If you can't prove it, doubt it.
IdiotsOpposite
Boom, headshot.
Ah, but I never said I don't doubt it. It's just my opinion that the circumstantial evidence in favor of RH being true is a lot more extensive than the circumstantial evidence for it not being true. Plus, I'd really like it to be true. But the other side gave off really convincing arguments. Hell, the whole debate was just interesting and fun to take part in.
ParadigmShifter
Random Nonsense Generator
Circumstantial evidence? Just one counter example would be enough.
IdiotsOpposite
Boom, headshot.
By circumstantial evidence, I mean analogs of the Riemann Hypothesis that have been proven. For instance, an analog of the Riemann Hypothesis for finite algebraic function fields was proven by Weil (in the quadratic case) and Deligne (in general). There are other examples, if you need them listed. And until that one counter-example is found, there's no proof that a counter-example does exist either. (And if it is found, I think it's likely that it'll be found by finding a minimum of Re(zeta(1/2 + i t)) above zero or a maximum of said function below zero, both of which have been proven would violate the Riemann Hypothesis, if they happened)
ParadigmShifter
Random Nonsense Generator
Mmmkay. You're obviously not as drunk as I am 
IdiotsOpposite
Boom, headshot.
Been sober for almost 20 years now.
ParadigmShifter
Random Nonsense Generator
I guess I'm your multiplicative inverse then
gangleri2001
Garbage day!!!
Thanks for ignoring my question.
ParadigmShifter
Random Nonsense Generator
About n-ary operators? They are just mappings.
"plus" can be defined as an n-ary operator, like in LISP (programming language), where
(+ 1 2 3 4) = 10.
"plus" can be defined as an n-ary operator, like in LISP (programming language), where
(+ 1 2 3 4) = 10.
gangleri2001
Garbage day!!!
So you basically provide the operator with the arity needed and that's about it? And what about the operator ?: ? Can you provide it with any arity other than ternary?
ParadigmShifter
Random Nonsense Generator
Nope, the ternary operator ?: (which is if/then/else for people who don't speak dialects of the C programming language) needs 3 arguments.
a ? b : c
means if a is non zero, return b else return c (in C anyway, in Java I think you can only test a boolean).
EDIT: Syntax for operators is a bit weird in C as well, I've seen the common error
if( a == b == c )
before, it doesn't do what people expect it to do (== is the equality test operator in C). However, a && b && c does work (&& = boolean "and"), with the caveat that it uses lazy evaluation.
EDIT2: Note: 0 == 2 == 3 evaluates to true in C
a ? b : c
means if a is non zero, return b else return c (in C anyway, in Java I think you can only test a boolean).
EDIT: Syntax for operators is a bit weird in C as well, I've seen the common error
if( a == b == c )
before, it doesn't do what people expect it to do (== is the equality test operator in C). However, a && b && c does work (&& = boolean "and"), with the caveat that it uses lazy evaluation.
EDIT2: Note: 0 == 2 == 3 evaluates to true in C
ParadigmShifter
Random Nonsense Generator
Depends on the operator. Looks like I have it wrong, == evaluates left to right according to this page: http://msdn.microsoft.com/en-us/library/2bxt6kc4.aspx
So 0 == 2 == 3 is false in C, but 2 == 3 == 0 is true
Should I open an ask a C/C++ programmer thread?
So 0 == 2 == 3 is false in C, but 2 == 3 == 0 is true
Should I open an ask a C/C++ programmer thread?
Mise
isle of lucy
Have you ever done any cryptography? I find that stuff fascinating. But I guess, like most useful things, it's more computer science than maths.
ParadigmShifter
Random Nonsense Generator
I haven't. There's quite a lot of number theory involved though.
civ-addicted
King
I did, and i really wanted to write my thesis in Cryptography, but there were no good Professor availible, sadly.
Cryptography is treated as a Pure Math subject at my university, and it's really close to Algebra and Number Theory. The methods used nowadays are based on unresolved problems in Math, namely the Discrete Logarithm and the Integer Factorization.
I even think that if you manage to solve this problems you might become kinda famous. Me and my friends used to joke about it that you could use this power for good (become famous) or bad (sell it to the Chinese for a buttload of cash). You could easily amass all money in world, cause all online accounts are protected this way.
I guess after all, it's like with physics. With all the applications you might oversee that fact that all is based on non-trivial Math, and they are lost without us
Rashiminos
Fool Prophet
Arity is another name for how many operands are used. It's a function that may operate on more than one variable..
For example, we could perform an AND operation on 4 boolean operands*. If all four are true, then the result of our operation is also true.
*Technically this is equivalent to 3 binary AND operations:
(A*B)*(C*D) ,
((A*B)*C)*D
'''''''''''''''''''''''''''''''''''''''''''''''
Alternative example: we could have an operation that takes a list of integers and return the largest value in the list (n-ary example that's comp sci related).
AE2: List of names, return the median name from alphabetized list.
Cryptography is treated as a Pure Math subject at my university, and it's really close to Algebra and Number Theory. The methods used nowadays are based on unresolved problems in Math, namely the Discrete Logarithm and the Integer Factorization.
I even think that if you manage to solve this problems you might become kinda famous. Me and my friends used to joke about it that you could use this power for good (become famous) or bad (sell it to the Chinese for a buttload of cash). You could easily amass all money in world, cause all online accounts are protected this way.
I guess after all, it's like with physics. With all the applications you might oversee that fact that all is based on non-trivial Math, and they are lost without us
With Shor's algorithm there is already a possible solution. There is just nothing that can calculate it, yet.
It is kind of funny that a lot of modern classical cryptography depends on the hope that we won't succeed anytime soon in building a scalable quantum computer.
