Video about Factorio

[kovarex]

I couldn't help myself, but I hear him talking about Factorio all the time
http://www.youtube.com/watch?v=Mfk_L4Nx2ZI

[Gammro]

That's a pretty interesting video. I was always wondering why 0! = 1, so this finally gave me an answer.

The continuous factorial in the end is also an interesting concept, I do fail to see how it relates to the factorial. Since, in my head, the factorial has always been based as "the amount of discrete configurations n objects can have"; as also seen in his given example with the coins. So it is supposed to be not "just" a function that also gives the same answers on whole numbers(/integers). *sigh* mathematicians... sometimes I don't know what the hell they're trying to do

[Nirahiel]

Ah numberphile, I love this youtube channel, and I've watched this video.
That blond guy has something I find fascinating, I dunno, he has a certain charisma I can't explain

[Math3vv]

i wish he was my math teacher :/
also i like the part when he divides 1 by 0 ands says "you have broken math, stop that"

Edit : watched other videos from that channel and now my head hurts ...

[Holy-Fire]

The continuous factorial in the end is also an interesting concept, I do fail to see how it relates to the factorial. Since, in my head, the factorial has always been based as "the amount of discrete configurations n objects can have"; as also seen in his given example with the coins. So it is supposed to be not "just" a function that also gives the same answers on whole numbers(/integers). *sigh* mathematicians... sometimes I don't know what the hell they're trying to do

Take exponentiation (taking powers) as an example. a^n is the number of different combinations possible of n digits with a possible choices. If n is not integer this combinatorial interpretation is meaningless, but you still have no problem using 4^2.5 to mean 4^2*sqrt(4)=32. The only logical way to extend the integer definition to real numbers is x^y = exp (y * ln(x)).

For factorials it is the same. Despite the definition of Gamma being completely different from the original definition of factorial, (the shifted version of) it is the simplest real function satisfying the same recursion rule (n+1)! = (n+1) * n!, and so it is the natural generalization of the factorial.

Example application: Perhaps you've heard of Newton's binomial expansion (a+b)^n = \sum_{k=0}^n a^k b^(n-k) n! / ( k! (n-k)! ). It turns out this expansion applies also when n is not an integer - the series is then infinite, and instead of the factorials you need to use the corresponding Gamma values.

Generalizations are prevalent throughout all of mathematics.

[Gammro]

Thank you for the explanation Holy-Fire, although I must admit I was a bit tired when I typed my reply at 4am. It's an interesting thing none the less, finding continuous functions for things we previously only knew as discrete.

[ssilk]

It would be someway cool to include the factorial-element more obvious into factorio. i think to the receipts. E. g. Receipt E needs 5 of receipt D needs 4 of C needs 3 of B needs 2 of A which needs 1 iron ore. Then the amount of iron ore to produce one E is 5*4*3*2*1 = 120

[Nirahiel]

Don't forget it's just a game, you don't have to know math to play

[ssilk]

Yeah, of course. But this one lies on hand. Perhaps, when this guy makes the next video about factorials he uses factorio to show that... No of course not,but who knows?

[Gammro]

Another video, and my mind is blown. I actually can't decide if I believe this is true:
http://www.youtube.com/watch?v=w-I6XTVZXww

If it's true, it's possibly the least intuitive mathematical concept I know. Meanwhile, my brain is trying to think where a mistake has been made, but I can't see it.

What do you guys think?

[kovarex]

What do you guys think?

It's trolling done the right way

[Nirahiel]

Nah, the guys at numberphile are really awesome

[kovarex]

Yes, but this is very clearly a joke.