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Mega A Level Maths Thread MK II

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Original post by reubenkinara
Because, I think: n!=(n+1)!(n+1)!n! =\dfrac{(n+1)!}{(n+1)!}

You sure about that bro? :erm:
Reply 2061
Avatar for tigerz
tigerz
Original post by reubenkinara
Don't mention it. Though, undoubtedly one of the more seasoned mathematicians on here will find some discrepancy with what I've written!


mmm..seasoned...sorry I love food haha! oh wells its all good

Original post by Felix Felicis
It comes from the gamma function:

Γ(z)=(z−1)!=∫0∞tz−1e−tdt⇒0!=Γ(1)=∫0∞e−tdt=[−e−t]0∞=1\Gamma (z) = (z-1)! = \displaystyle\int_{0}^{\infty} t^{z-1} e^{-t} dt \Rightarrow 0! = \Gamma(1) = \displaystyle\int_{0}^{\infty} e^{-t} dt = \left[ - e^{-t} \right]_{0}^{\infty} = 1

At least I think. Where are you L'art? :tongue:


Sorry, I failed to understand any of that LOOL, never seen them signs haha, long story short 0!=1 I shall remember that
uhm... Where are you art?.. me lost
Original post by tigerz
mmm..seasoned...sorry I love food haha! oh wells its all good



Sorry, I failed to understand any of that LOOL, never seen them signs haha, long story short 0!=1 I shall remember that
uhm... Where are you art?.. me lost

Hmmm. Try this link.
Original post by tigerz

Sorry, I failed to understand any of that LOOL, never seen them signs haha, long story short 0!=1 I shall remember that
uhm... Where are you art?.. me lost

Don't worry, it's unlikely you will have, but if you get bored, it's called the Gamma function, have a read :tongue:

And I'm referring to another TSR user - he's an amazing mathematician and in love with the beta and gamma functions. xD
Original post by Felix Felicis
It comes from the gamma function:

Γ(z)=(z−1)!=∫0∞tz−1e−tdt⇒0!=Γ(1)=∫0∞e−tdt=[−e−t]0∞=1\Gamma (z) = (z-1)! = \displaystyle\int_{0}^{\infty} t^{z-1} e^{-t} dt \Rightarrow 0! = \Gamma(1) = \displaystyle\int_{0}^{\infty} e^{-t} dt = \left[ - e^{-t} \right]_{0}^{\infty} = 1

At least I think. Where are you L'art? :tongue:

http://en.wikipedia.org/wiki/Empty_product
http://en.wikipedia.org/wiki/Factorial#Definition

It seems to be defined rather than proven, and any 'proofs' I have come across have been shifty at best.

e.g. Where n!n=(n−1)!\displaystyle\frac{n!}{n}=(n-1)!
Let n = 1 and 1!1=1=0!\displaystyle\frac{1!}{1}=1=0!
But the equation itself necessarily assumes that n≥2n\geq2 so that (n−1)(n-1) can actually be a factor.
(edited 10 years ago)
Reply 2065
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tigerz
Original post by reubenkinara
Hmmm. Try this link.


Thank you :smile: I will spend my Friday night reading that haha :wink:


Original post by Felix Felicis
Don't worry, it's unlikely you will have, but if you get bored, it's called the Gamma function, have a read :tongue:

And I'm referring to another TSR user - he's an amazing mathematician and in love with the beta and gamma functions. xD


Added to the list! Oh I see :smile:

Also Joostan I redone the log question from earlier in less than 5 mins WOOP! You is a sick teacher :ta:
(edited 10 years ago)
Original post by The Polymath
http://en.wikipedia.org/wiki/Empty_product
http://en.wikipedia.org/wiki/Factorial#Definition

It seems to be defined rather than proven, and any 'proofs' I have come across have been shifty at best.

e.g. Where n!n=(n−1)!\displaystyle\frac{n!}{n}=(n-1)!
Let n = 1 and 1!1=1=0!\displaystyle\frac{1!}{1}=1=0!
But the equation itself necessarily assumes that n≥2n\geq2 so that (n−1)(n-1) can actually be a factor.

True :redface: It may just be the definition :dontknow: Going by the definition of the number of ways we can arrange n objects, I suppose there's only 1 way you could arrange an empty set, hence 0! = 1? xD
Original post by Felix Felicis
True :redface: It may just be the definition :dontknow: Going by the definition of the number of ways we can arrange n objects, I suppose there's only 1 way you could arrange an empty set, hence 0! = 1? xD

That's what LotF proposed as an explanation too :yy:
Original post by joostan
...

She wants the D bro :sexface:

Original post by The Polymath
That's what LotF proposed as an explanation too :yy:

Awesome! xD
Original post by Felix Felicis
She wants the D bro :sexface:



Usually when I ask for subject help I'm trying to avoid the D. :teehee:
Original post by Felix Felicis
That's what I feel anyway comparing BMO2 and STEP I, although I haven't had much experience with STEP II/III


I'm thinking if I can qualify for the IMO, these asians can train me good which should help out with STEP as well :colone:
Original post by The Polymath
You sure about that bro? :erm:


Of course! Everyone knows n!=1 ∀nn! = 1 \ \forall n

You need to brush up on your maths basics, bro :no:
Original post by justinawe
I'm thinking if I can qualify for the IMO, these asians can train me good which should help out with STEP as well :colone:

A user called Mladenov on here who's come very close to qualifying for the IMO for Bulgaria says the STEP questions are very accessible for him. :tongue: If you could qualify for IMO, you'd likely smash STEP. xD
Original post by justinawe
n!=1 ∀nn! = 1 \ \forall n

n!=1 ∀n∴0!=1n! = 1 \ \forall n \therefore 0! = 1 :colone:
Original post by Felix Felicis
x
Seems legitimate.
(edited 10 years ago)
Reply 2074
Avatar for FeMn
FeMn
3
Original post by justinawe
Didn't the question ask for 4 digit numbers only?

If not, apologies for my mistake :redface:


naah it said greater than 4000 with no repeats:smile:

have you done jan 13?
Original post by The Polymath
n!=1 ∀n∴0!=1n! = 1 \ \forall n \therefore 0! = 1 :colone:Seems legitimate.

Reminds me of this joke. xD
Original post by Felix Felicis
A user called Mladenov on here who's come very close to qualifying for the IMO for Bulgaria says the STEP questions are very accessible for him. :tongue: If you could qualify for IMO, you'd likely smash STEP. xD


I'll probably need to spend a little more time on The Proof Is Trivial thread for IMO kind of stuff, I guess :holmes:

I highly doubt I'll qualify though, even if may be a little easier to do so here.
Original post by FeMn
naah it said greater than 4000 with no repeats:smile:

have you done jan 13?


Jan 13? What exactly do you mean by that?
Original post by Felix Felicis
Reminds me of this joke. xD

Sorry, but this says the opposite.
Jkn
x

Oh hi.
Reply 2079
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FeMn
3
Original post by justinawe
Jan 13? What exactly do you mean by that?


the january 2013 paper aha:smile:

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