Category: School

nothing much really happened today. got a lot of hw done and etc. no new anime. sigh…

but here’s something for you to ponder upon. in mathematics, 2 sets of numbers are said to be the same size if u can match up one # from each set all the way to the end. do u still follow? cause the next step will jump out like you crazily. at first i was shocked too and tried to disprove it, but according to mathematics if there exist ONE one-to-one function between 2 sets of #s, then the domain and range are the same size. think about this D:{set of all even #s} and R:{set of all odd #s) and with the function f(d) = d+1 = r; then that’s a one-to-one function mapping evens to odds; therefore both sets are the same size. what threw me off was when liam said that the set of integers and the set of natural numbers was the same size. i was like no way! the set of integers is like 2x the size of the set of natural #s. my grounds was that the set of integers include the set of natural #s (i’m still standing for this pt, although after our TA/GSI told us that liam was correct, i’m just making a fool outta myself). the thing is we can map the set of integers onto the set of naturals with a one-to-one function. think of this function where:

f(d) = {
  (d+1)/2 if d is odd;
  (-d)/2 if d is even;
}

this function maps every single integer you give it, onto the set of all natural #s. think about another equation. the set of all real #s between 0 and 1 exclusive and the set of all real #s greater than 1. they are the same size although the set of it’s obvious (or as liam says, you’ve been fooled) that the set of real #s greater than 1 is larger than the set of #s between 0 and 1 exclusive. lets try the function f(x) = 1/x. Throw in any real # greater 1 and you’ll get a corresponding real # between 0 and 1. throw in any # between 0 and 1 and you’ll get a # greater than 1. no matter what # you try, this will always work.

now i come to my hypothesis. since you can use one function to prove this true, why can’t i use one function to prove it’s not true. such as the set of positive reals and the set of all reals. since i was easily fooled to see the set of reals is 2x the size of the set of positive reals, i went ahead and found the function f(x) = x*x. Given any real #, i will always get back a positive real #, but the phenomenon is that there is exactly 2x the # of inputs than outputs meaning i can get 9 with +/-3. meaning i’ve found an equation which has shown that the size of all reals is actually twice the size of positive reals. liam says i can’t do this because you can easily find a function to disprove anything, but those are just specific cases. the main thing is that if there exists at least one function that maps it from one-to-one, the it’s the same size. i sort of get what he’s trying to lead at, but there is that gap that i see increasing as u approach infinity. anyone wanna prove or disprove this? hehe.

for those that was bored with my semi-lecture, check out this link link. that girl is amazing and this link was donated by AznEECS. g’nite ^_^x

one of the hilarious things happened in my cs70 class yesterday. we were learning about stable pairings and to show this, our lecturer had this little demonstration. he asked for volunteers and 6 guys went up. well, the game goes like this. there are 4 guys and 4 girls and they want to find the configuration which will give them the most stable pairing of all. the thing was they needed to list their preference from 1 – 4 of the other group. The 2 groups were {boy 1, 2, 3, 4} and {girl 1, 2, 3, 4} and the lecturer even asked why several ppl chose that configuration. one said, i’d definitely not chose 3 cause he looks weak. REMEMBER, this was 6 guys in the front. it was hilarious, after they had their preference on who they wanted to marry (both boys and girls who were acted by guys had their preferences). so round 1 came, the setting was set in the medieval ages where boys would come to the girls tower and kneel down and propose). this is how it works, if the boy proposing is higher on her preference list than the one she already has, she kicks the previous one away and accepts the new one. If not, she just rejects him. So the guy goes through all of his entire list of preference until he finds a stable pairing. our job was to prove that given n boys and n girls, that there will always be a stable pairing. and sure enough, there will always be one.

good news guys. i’ve updated both the picture of the week and added a ton of new doodles. enjoy ^_^x

the 9-11 front page will be left for one more day. since my report is still about 9-11. thanks to elbandmonkey, who showed me this link. Backup of it is here in case the original link changes. If you still don’t see what’s so obvious, highlight the following invisible line it says: the winning lotto #s of NUMBERS: 9,1,1. Coincidence? or Fate? i’ve gotta say tho, that i’m glad nothing serious happened today. peace!

anyway, our bathroom has finished being tiled. but still unable to use it yet since the tile needs to dry and harden. he says we should be able to use it on friday. sigh… i’ve been washing my hair in the kitchen sink for the past few days. sigh…

currently doing my cs70 hw which is due tomorrow. so gotta get back to work. only 1 class tomorrow! w00h00! ^_^x