Blue Ray my opinion, Non measurable set

I just finished watching Michio Kaku's documentary on time interesting documentary.It is one of the dozens of DVDs which my good friend Murat gave me during Christmas brreak. It tincludes all the Planet Earth episodes and documentary on time etc. I liked the kaku's demonstration of time as a unit of distance. It was impressive because his whole life of some 50 something years was within some foot of the table in his home in New York but its totally insignificant compared to the life of earth which stretches to distance between New York and San Fransisco.

I am surprised that Sony is still pushing DVD blue ray technology to me it just doesn't make sense. The two bulkiest part in computer are DVD drive and hard disk. With the falling price in semid conductor memory both of these can be eliminated with one stroke. DVDs use that mechanical technolog whih because of wear and tear is a big hindrance. Its a technolgy which is a spiced up CD technolgoy with better software and compact data but the concept is still the same burning land and pits to store the data. The falling cost of electronic memory makes them a viable contender. I know the hollywood will be a little reluctant to embrace this because it will make them open to being copied easily but then all DVDs are ripped the next day and distributed electronically. I envision a future in another 5 years when the need for lap top computer is eliminated because all the functions for which we need laptop can be done with the cell phone. The cell phone will make use of broad band internet and are off the hook of cell towers. They can be seamlessly connected to television and large screen devices with technologies like blue tooth

Today I woke up early and my mind was still buzzing with the analysis. I had a strange dream where I did see Dr. Feinsilver and Dr. Budzban. It was kind of some exam and I was carrying my ST. Microelectronics folder. I remember placing that on dusty floor. I entered into examination hall which has a huge sliding door and I pull it open trying to make as little sound as possible but then I had to confront with not knowing my seat number. It was a huge number and I was wondering whiy they had to have such a huge number. I don't know but at the back of my mind I thought they didn't have enough students taking the exam it was some 10 or 12 digit number and half way through I was fumbling and wanted to go out to check my name against the number. It was a early morning dream and that's all I can recount at this time.

I attended the Buddhist rso meet today. Today's session was conducted by Dr.Julie Stein and there was only one more person was there. We went over 5th precept of not being mindful, vegetarianism, avoiding alcohol and being careful with watching television. It's a series of lectures given by the Vietnamese Buddhist monk Titch nacht han and I tend to agree with lot of his vies. In the morning I had appointment with Letti at the Dental Clinic. Today she worked on half of the mouth, cleaning every tooth diligently. In the evening around 16 hrs I had another appointment when she too 18 X-Ray pics of my mouth. Letti being so generous used her coupon to get me the free X rays. Otherwise it costs almost $100 if I go outside. Thanks Letti I really appreciate that gesture. In my Business Calculus class today I taught more on different techniques of Integration. I also took my laptop to demonstrate Riemann Integral and its significance using Maple Example and Geogebra Applet.

In my Real Analysis. I covered the measurability of function. The definition has 4 equivalent forms. The easy way to state it that a function f is measurable if the domain E is measurable and the set {s belongs to E, f(x) > alpha} where alpha belogs to R. The other 3 sets are f(x) >= alpha, f(x) < style=""> then use the property of union and intersection is Lebesgue measure. Note the set we are looking for the function to be measurable.

One more thing I would like discuss is the idea behind the proof of non measurable set. First we take a set [0,1). Note its open on one side. The measure for this set is 1. Lets partition the set in such way that two elements are equivalent if their difference is a rational number and the difference between any two numbers of different equivalent class will be an irrational number . Its easy to notice that there will be one partition which contains all rational number and the other partitions will consists of irrational number. Now construct a set P by choosing one element from each of the partition. Now we know that rational numbers are countable. Lets take each rational number between 0 and 1 and add construct sets like Pi = P + ri. For ex P0 = P+ 0 when 0 is added. Now this addition is modulo addition 1 . So if P+ri is greater than 1 than we subtract 1 from the sum. As set of real number is translation invariant we see that the union of all sets will give us the set {0,1) Also all these Pi's are either disjoint or same. To prove that assume there is an element x which belongs to pi and pj, i.e x = pm = rm = pn+rn => pm -pn = rm -rn, but rm-rn = rational. Therefore pm – pn = rational however this cannot be possible because if two numbers differ by a rational then they have to be in same set. Thus two Pis cannot share an element. Now all Pis are distinct which means the measure of each of these sets is either zero or finite. Note all that each of these sets have the same measure and since rational numbers are countable. If we add the either we add 0 infinity times or some constant infinity times. In first case we get a zero and in 2nd case we get an infinity. However the set has measure 1. So we have a contradiction. The thing I need to convince myself is that the union of Pis gives us the whole set [0,1).