And hopefully here to stay, for real, seeing as I don’t have a lot going on in my life right now. I’ve just come back from New York, and my freshman year is over… WWHATTTT. It’s been epic and I can wait for next semester. Summer break is 3 months… so yeah, I’ll probably keep posting here and there. I actually really am sorry that I haven’t posted at all since September 18th 2015. Put into perspective, that’s 247 days ago, it really has been way too long. So, I don’t yet know what I’ll be posting about, I guess we’ll find out sooner or later, maybe a few maths-ey posts, maybe a few on life in New York, and the places I visited… I think it’ll depend on my mood and all the rest. But don’t worry, you’ll definitely hear from me! And of course, if you’d rather not hear about my life (which would be very understandable) its easy to unfollow me, but I mean, New York is pretty cool even if I’m not, so I’m sure there’ll be at least some things worth reading.
So, see you in a few hours/days I guess…
Okay, so I know I said I’d be posting often after the last post, but I kinda misjudged how much time settling into my new home in New York would take!! So this is my third week here and it is absolutely AWESOME! Continue reading
It HAS been too long, my last post was like, what? over 2 months ago?! I’ve been so busy though, its all been really exciting (but scary at the same time) getting prepared for university and all that. So, I’ll tell you what I’ve been up to recently… (in the months that I didn’t post)
Take out those hidden pizzas, this will be a long story…
Gosh, I’ve not written many posts the last few weeks…what is wrong with me? Yep, that would be EXAMS. Ahhhhhhhhh! Yeah, you probably get the message. My A2 exams have started… and that’s why blogging has not been my top priority for the past few weeks. I’m actually really sorry, because I do love writing posts (and there’s an added bonus: it helps me study). Nevertheless, today is Saturday, and I just need a break from all this studying so what better way than to write a post on exam stress/ how to successfully go through the exam period (or really just what makes you stress during the exam period…)?!
This post is probably late for most exam-takers. I know IB exams have finished, as have American SATs and finals, GCSE’s and IGCSE’s nearly have, and the same goes for AS levels. So basically A2 exams are the only ones left. For some of you, exams may even be non-existent at the moment! However this will come in handy whenever you have something big to prepare for! P.S. There are quite a few GIFs in here so it may take a while for them to load, but they’re really funny so just be patient! Continue reading
I can hear you thinking: “Jeeeez! She’s been gone a long time!” and I know, I know…it’s way past time that I did another post. I’m sorry that I disappeared so suddenly and that I’ve been so inactive/quiet/not posting for such a long while, but my exams start in one and a half weeks and its scary. Time is passing way to quickly nowadays.
Okay. My disappearance wasn’t quite as dramatic as this I must admit. But still…
So, as i’m in that revision/study kind of mood, I’ll be breaking down (some of) Further Pure 2 for you (FP2 is part of my maths course) 😀 enjoy!
A factorial is the product of an integer and all the integers below it i.e. factorial four ( 4! ) is equal to 24 (= 4 x 3 x 2 x 1) But if this is so, why is 0! = 1, because technically, 0! = 0 x 0 right? So WHY??
If n! is defined as the product of all positive integers from 1 to n, then:
1! = 1 x 1 = 1
2! = 1 x 2 = 2
3! = 1 x 2 x 3 = 6
4! = 1 x 2 x 3 x 4 = 24
and so on…so, n! = 1 x 2 x 3 x … x (n-2) x (n-1) x n
Logically, n! can also be expressed n x (n-1)! .
Therefore, at n=1, using n! = n x (n-1)!
1! = 1 x (0)!
which simplifies to 1 = 0!
When thinking about combinations we can derive a formula for “the number of ways of choosing k things from a collection of n things.” The formula to count out such problems is n!/k!(n-k)! For example, the number of handshakes that occur when everybody in a group of 5 people shakes hands can be computed using n = 5 (five people) and k = 2 (2 people per handshake) in this formula. (So the answer is 5!/(2! 3!) = 10).
Now suppose that there are 2 people and “everybody shakes hands with everybody else.” Obviously there is only one handshake. But what happens if we put n = 2 (2 people) and k = 2 (2 people per handshake) in the formula? We get 2! / (2! 0!). This is 2/(2 x), where x is the value of 0!. The fraction reduces to 1/x, which must equal 1 since there is only 1 handshake. The only value of 0! that makes sense here is 0! = 1.
And so we define 0! = 1.
Well, I hope that was interesting! And I feel like I have to add something more interesting into this post sooo…
I never knew you could do this! Interesting!
Well, I guess I can’t say ‘stupidity at the next level’ because, you know, they are doing maths so…
See you all next time! Keep smiling and thanks for reading!
Today will be a good old fashioned ‘hand written’ post (ie photos of my hand written pages!) on complex modulii. Let us begin…