Friday, April 17, 2009

 

Infinities and Aparna's bijective map

Infinity, as the name suggests, is that which is not finite. The concept is a bit scary, not easily understandable. First time when I heard about it in mathematics, I was thrilled. Later when my programs started entering into infinite loops due to bugs, I started hating infinity. I even thought of leaving my programs to run for infinite time trying to understand what infinite time means. Seriously, I was so stupidly curious at that time. Soon after I left programming, I started loving infinity again. As I thought more and more about infinity and after reading the quote by Einstein, "Two things are infinite: Universe and Human Stupidity; I am not sure about the former", I defined a relation between stupidity, love and infinity. To understand that, you must understand the several kinds of infinities.

There are infinite types of infinities. Basically one needs to understand 2 kinds to understand infinite kinds. First consider a countable infinite set N = {1,2....infinity}. Then 2N = {2,4,....infinity}, which is same as removing alternate numbers from N. But since we can define a bijection(injective & surjective map) from N to 2N as f(x) = 2x for all x belonging to N, the cardinality (number of elements) of 2N is same as that of N. Therefore, the two sets are of same infinite order. A power set of a set is the set of all its subsets. Cardinality of the power set of a set with n elements is 2 power n. Obviously there can't be a bijection from a set to its power set, because the power set has more (means 2 power n) elements. Following this logic, power set of N mentioned earlier has cardinality 2 power infinity. Hence 2 power infinity is the immediate bigger infinity than our good old simple infinity. Now consider the power set of the power set, cardinality of which is 2 power 2 power infinity. Extending this infinite number of times, we find that there are infinite types of infinities.

Recently I have come up with a bijective map.

Let X be a set defined as X = {stupidity, love} and Y = {infinity, 2 power infinity}.

f:X->Y defined as ,

f(stupidity) = infinity, -----(1)

f(love) = 2 power infinity

= 2 power stupidity {from (1)


# posted by Aparna @ 3:28 PM 4 Comments

Wednesday, April 01, 2009

 

Can you "C"?

Caution: I am egocentric and egotistic. No, a better word for me is "narcissist". This is yet another blog centered around myself.
People often ask me the expansions of "C" and "K" in my name, which are "Chakrakodi" and "Krishnashastry" respectively. The next question is where's this place "Chakrakodi" or whether it is a place, for which no one on this earth probably has the answer.
Actually, "C" can be interpreted in lot more interesting ways: Creative, Credible, Connoisseur, Confident, Conqueror, Conscientious, Curious etc. "C" in my name does not mean any of these. I like to associate my "C" primarily with the following three things:-
1. Correlating (the Coincidences),
2. Confusing (even the Close friends), and
3. Contradicting (myself).
Ever since my 6th semester engineering, I've been hearing, "You are Complicated". Surprisingly, it took them so long to find out; I knew it much earlier. Complicated minds have the ability and inclination to Correlate even the unrelated things and situations. Not just that, they have a passion for jumping to Conclusions based on these Correlations, even if they know that more often than not, these are wrong. Reading between lines, finding patterns in numbers, interpreting incidents to be signs of some significance, and finally based on these, Coming up with weird theories and Corollaries. {I am a highly impractical and philosophical individual with absolutely no sense for my priorities.} Many a times there's no Correlation between what I think, say and do, rather there are Contradictions. In this way I become an enigma to those around me. If they try to understand me by applying my own theories on myself, they are bound to get Confused. Hold on, you must believe that the following sentence in the next paragraph is true.
All of the above is false. Can you "C" that?
Happy Fools' Day..

# posted by Aparna @ 11:38 AM 6 Comments

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