[lim_x->c f(x) = lim_x->c g(x) in {0, -∞, +∞}]^∃[lim_x->c f'(x)/g'(x)] => lim_x->c f(x)/g(x) = f'(x)/g'(x) is pretty nice. <3
common sense doesn't need a name
True. And I'm extremely sorry. :(
$ xterm -geom 159x100 $ ghci Prelude> let f = 1 : 1 : zipWith (+) f (tail f) in take 780 f
See anything interesting?
It should work with any language... If you don't have Haskell you could try it in Ruby with
$ irb
irb(main):001:0> def f(n); r = [1,1]; 2.upto(n-1) { |i| r << r[i-1] + r[i-2] }; r; end
irb(main):002:0> f 780
Fibonacci numbers are awesome :)
> ^∃
i don't understand the notation at all, bluet; is this a statement of l'hospital's theorem?
i don't understand the notation at all, bluet; is this a statement of l'hospital's theorem?
http://en.wikipedia.org/wiki/Logical_conjunction
http://en.wikipedia.org/wiki/Existential_quantification
yeah, i think it's the theorem.
http://en.wikipedia.org/wiki/Existential_quantification
yeah, i think it's the theorem.
It's supposed to be. I attempted to translate Wikipedia's definition with words.
is there an operator that means " has the same sign as " ?
one way to do it is this:
ab > 0 <=> "a and b have the same sign"
but i want a cleaner way that looks like this:
a [operator] b
one way to do it is this:
ab > 0 <=> "a and b have the same sign"
but i want a cleaner way that looks like this:
a [operator] b
the fun way to say "ab > 0" is "a and b are on the same side of zero." it makes me smile. :)
I think you could say "a, b > 0".
i think "a, b > 0" means "a > 0, b > 0"
Isn't that what you meant? It's like saying "both are positive".
Oh, I see, "both are negative" should be true too.
I guess for clarity you could use "sgn(a) = sgn(b)" where sgn is the signal function.
sgn x | x < 0 = -1
| x > 0 = 1
| otherwise = 0
:) cool, will do. i might call it "sign()", but "sgn()" is nice because it works for "sign" and "signal."
i used the sign() function in my thesis theory section in order to allow for ordinal ranking of outcomes whose expected value is less than zero:). mu is expected return from an outcome. tao is stochastic standard deviation. mu and gamma are preference parameters.
expected utility = U=sign(mu)|mu|^theta-tao^gamma
how impossible would it be to get code that compiled equations in posts to latex dynamically? just thinking it would be pretty awesome.
expected utility = U=sign(mu)|mu|^theta-tao^gamma
how impossible would it be to get code that compiled equations in posts to latex dynamically? just thinking it would be pretty awesome.
probably not extremely difficult
Or you could add MathML support.
yeah, i was looking at that, too.