Tuesday, December 4, 2007

You Complete Me


Please note this was created entirely after karaoke so im slightly drunk. Also look up the mathematical definition of completion or Cauchy sequences to understand this. A drunken explanation is...
The completion of a set, is a bigger set (or itself) such that all Cachy sequences converge in this set. A sequence which converges is a sequence of numbers... say 1, 2, ,3 ,4... is a sequence... though a sequence which gets closer and closer to anotyher point in the set... say 1/2, 1/3, 1/4, 1/5, ... gets closer to closer to zero. so it converges to zero in real numbers.. however is it only cauchy in positive numbers since it gets closer and closer to a number which isnt in the set. Ok so a sober explanation would be better. But you get the jist
and example of completion.... Take the set of fractions.... there is always a number between any two fractions which cannot be expression as a fraction... so teh set of all (real) numbers is the completion of the fractions.. since it fills in the gaps essentially... so all cauchy sequences converging in the combination of two sets implies that one set it the completion of the other.
Jason... you shouldnty have told me to make another comic when im drunkish... remind me and i'll think of one people will get tomorrow...
N.B.
All non-convergant Cauchy sequences in me, converge to something in Mel. :)
I like this one :D... she's a keeper. Any thats the plan!

2 comments:

Steve said...

I'm such a tool! lol

Jason said...

Bahaha, beautiful. :-P