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+--- Thread: From addition to multiplication? (/thread-3124.html)
RE: From addition to multiplication? - AFtExploision - 04-23-2014
Abandon dcents!
RE: From addition to multiplication? - David - 04-24-2014
(04-23-2014, 09:57 PM)AFtExploision Wrote: Abandon dcents!
That's a better idea.
RE: From addition to multiplication? - greatgamer34 - 04-24-2014
Abandon hope ;-;*
RE: From addition to multiplication? - Konstacon - 04-26-2014
I found a way. As an exit slip of ORE, here is my way. First, let function f map a factorial to its number, like f(120) = 5. If I use normal math terms it'd be f: x! → x. Now, the binomial coeffecient of n and k is n!/k!(n-k)!. This can be represented differently, but let's use this definition because it has (n-k)!. In order to remove that ugly n! numerator we multiply the coeffecient by 1/n!. To remove the k! at the bottom, we multiply everything by k!. Now we have k!/n! * binom(n,k) = 1/(n-k)!, so let's do 1/binom(n,k) to get (n-k)!. Now we have n!/k! * 1/binom(n,k) = (n-k)!. To simplify this, we can remember reciprocals from pre-algebra (did that two months ago, fuck prealgebra) and we know a * 1/b = a/b, so we'd get (n!/k!)/binom(n,k) = (n-k)!. Now, remember our function f? To map (n-k)! without using subtraction, we do f((n!/k!)/binom(n,k)) = n-k. Now to transform n-k to n+k? Simple; take the conjugate of this. Writing this in equation form makes:
Well I'm lazy, go onto http://www.codecogs.com/latex/eqneditor.php and type in f\overline{\left (\frac{n!/k!}{\binom{n}{k}}\right )}=n+k in the thing. The line over everything is the conjugate symbol. Take that aft!
Fuck... nobody will understand my post I just realized.
RE: From addition to multiplication? - Konstacon - 04-27-2014
fuck.
RE: From addition to multiplication? - Iceglade - 04-27-2014
(04-15-2014, 03:53 PM)David Wrote: Is there a way to write a+b without using addition?
Notice he didn't say anything about method of evaluation :3
RE: From addition to multiplication? - David - 04-27-2014
Huh?.
RE: From addition to multiplication? - Konstacon - 04-27-2014
(04-27-2014, 08:55 PM)David Wrote: Huh?.
He's saying the area under the curve f(x) = 1 from a to b, which is b-a, or b+(-a)
RE: From addition to multiplication? - Iceglade - 04-28-2014
Obviously if you were to evaluate it you would have to use the fundamental theorem of calculus and subtract anyway (and you subtract in some quantity in all the numerical methods too), but the general presentation doesn't imply any kind of additive relationship. (Since it's a rectangle, it almost feels more like multiplication).
RE: From addition to multiplication? - David - 04-28-2014
I'll just let you two figure it out, I'm outta here.