Randomness

[mayoraasei]

Why does there have to be so many molecules and receptors in the immune response? ==; And apparently this is "the easy version". ARGH.

And they all have numbers attached ToT I hate it when they go up in numbers and have vastly different functions.

Because I was incredibly bored yesterday, I proved mathematically that squaring any number ending with 5 would be the product of the digits before the five and the digit before five plus one, and then add 25.

Okay, that didn't make any verbal sense ==;; (I.e. 25² = 20x30 + 25)

Well anyway, I cackled for a while and then realised I don't study maths ==;

Oh, and the proof could easily be done by anyone in year 9.

Hey Jenny, how would you prove that the addition of the digits of any number divisible by 3 must itself be divisible by 3?



I shall endeavour to break 3 million NP in the next few days ^-^

I'm wondering if I should invest in my Neohome (i.e. furnish and build. Though not in that order.) or if the enthusiasm is brought on by procrastination.

Comments

[jezjezjezza.livejournal.com]

:)! ooh! yeah that works for any number of preceding digits in your positive integer too :D

oh fenglet, you should have done number theory with me, you would have loved it *sigh* (plus you would have protected me from that awful karl guy (teehee, I have ulterior motives for wanting you to have done number theory with me!))

um, here's a proof of that, although it's rather hand wavy..

let n be a positive integer such that 3 divides n and some power of 10 divides n as well

write n=(10^k)*X, for some (positive) integer k, and some 0<= X < 10
3 doesn't divide 10 so 3 divides X (because 3 divides n by assumption)

i.e. X=3*y for some integer y
(note, y=0,1,2 or 3, and X=0,3,6,or 9 is the first digit of n.. so n looks like "X00..00")

so n=(10^k)*3*y

let n1, n2, .., ns be numbers of the above form

let the positive integer N=n1+n2+...+ns

for some ni=(10^ki)*3*yi, for some integers ki and yi (I'm using i as a subscript.. but it looks crap in text ^^')

such that each ni is divisible by a different 'highest power of 10' (ie. the ki are different.. so we can look at the digits of N seperately)

without losing generality, let's pick 3*yi to be the ith digit of N..

then 3*y1 + 3*y2 + .. + 3*ys = 3*(something which is also an integer)

^__^ that's how I'd prove it, but there's prolly a neater way ^^'

ooh! you're gonna break 3 million? ^O^ sweet! yeah, invest in your neohome! if I had more np I'd do so (but I don't, so I won't ;D)

[jezjezjezza.livejournal.com]

oops, I should have mentioned N is divisible by 3 by assumption too ^^'

[a-cryptic.livejournal.com]

Hmm, I've been meaning to post this under the correct post.... however, you either don't have an entry concerning your new layout, or I'm simply blind and can't find it =p. But newai, love your new layout!!! ^^. I feel inspired to un-neglect mine... but I have a sneaky suspicion it will continue to be sorely neglected XD... we'll see, lol *runs away*

Oh oh!! btw, good luck for your upcoming exams this coming week!!! Look forward to self-inviting myself to your place to watch anime in the holz, OR you can come to my place!!! I so love my new computer *huggles it*

Hmm, I think I'll stop hogging this computer now and let my sis have a go....

[beliael.livejournal.com]

Bah RECEPTORS. Studying for neuropsychology is KILLING ME, there's so much crap to remember about neurotransmitters stuff. UGH.

[luna-rainbow.livejournal.com]

OMG, don't you just love how there's like, 5 receptors for muscarine, 5 for nicotine, and about 10 for adrenaline, and another 10 for noradrenaline, and about two dozen for GABA, dopamine, substance P and the crap?

And they all have such frustratingly different effects.

And then there's only about 200 drugs they cram into you, each with different specificity at different sub-populations of receptors thus causing different effects and different side effects and has multiple chemical and pharmaceutical and common names...==;

I share your pain ToT

I'm currently looking at my bronchodilator lecture...I don't understand anything ToT It's all fuzzy pictures. What's calmodulin? And MLCK(PO₄)_(i)? ToT