Thursday, September 02, 2004
Ahhh... the nice wind... the rain... heaven on earth... haha no not the tea... hahahha darn... that wuz really spastic... haha anywayz i confess... I SKIPPED SET THEORY lecture today!! haha i mean the sky wuz beckoning me to return home for my slumber... haha... ok fine... i have a weak mind... haha i'm a sucker for temptations like this... haha
anyway, haven't really blogged for a long while... actually, haven't really come online for a long time... so here i am... trying to write something... haha oh oh US OPEN is currently in progress... so far hewitt nalbandian davenport and of course HENIN HARDENNE is on track to progress thru the ranks... AND!! amazingly henman beat karlovic in the first round!! excellent!! i wuz sooo sure henman would be out since karlovic is renouned for causing upsets... haha way ta go tim!! wooo... haha just hope he doesn't lose steam... haha
hmmm proof for today arr... hmmm nothing much... so i guess i'll resort to give a rather over used and common proof that the collection of all sets is not a set... haha
Claim: The collection of all sets is not itself a set.
Proof. Assume, for the sake of contradiction, that there exists a set of all sets we call A. Now, by the axiom of comprehension, we define another set B:={x ε A : x NOT ε x}. But B ε B iff B ε A and B NOT ε B. Since A is the set of all sets, clearly B ε A is always true, and the statement reduces to B ε B iff B NOT ε B which is a contradiction.
hmmm... i feel so cheapskate after giving such a simple proof but then again.. haha i dun understand the proofs in number theory yet... haha especially those heavily involving dirichlet products and big Os... haha
ok la... enuff for today... gotta rush to produce QTS and KKM tutorials... b4 taking a book at set theory again... haha ciao...
Rain Rain Rain... so hopefully sunday will be bright hot and sunny!! tanning time!! haha
haha quite healthy except for some oily foods here and there... haha like KFC... haha oh oh had Genki Sushi today... not exactly healthy but at least i confessed... haha...
{9:08 PM}
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