Tuesday, May 15, 2007

Sybil Problem

What I think...
Well thinking about todays class and what we learned. I guess in a way I can relate Sybil to limits. In one hand Sybil, mathematically, can never get to the other side of the room because it would always have left have of what it has remaining to go. In other words every time Sybil moves forward, although it has achieved some space, it still has half of what is left of the room to go. He will always have room to go. That is because limits can never be exceeded nor achieved. In todays class we were said to think of limits as boundaries that may or may not reach it. For me the Sybil question has a boundary of infinity. It has no limit. DNE. I dont know if this is right, I am just stating out my ideas.
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3 comments:

Bee Bustillo said...

Mely, I think your idea is good. In my class, DC also had a similar answer and I agree with both of you guys. It's great that you could relate what you learned in class, which is a new topic, to the Sybil question because I think it has a lot to do. Another thing. I think it's great that you at least thought about the question and tried answering it. I don't think right now matters if you answered it correctly or not. I think that what counts the most is that you analized and came up with your own answer. That demonstrates that you are dedicated, or at least want to improve with your mathematical skills and analizes. Good job!

May 16, 2007 at 2:12 PM
anto said...

Well, a limit is, as you stated, a boundary. You can think of a boundary as a wall that the sequence would eventually either run into, or get really close to. The sybil question does have a limit, the limit is the size of the class. Even though sybil will never reach the end of the trailer, he will get infinitely close to the end. Think of it as a series with each term signifying the distance sybil has crossed.

(1/2), 1/4, 1/8, 1/16, 1/32, 1/64......etc

Now in order to find whats the limit of sybil's movement then we need to ad all the terms in the geometric serers. This seems hard to do though because there are an infinte amount of terms. Lets look back at the sum of a geometric series formula:

S= t1 ((r^n-1)/(r-1))

In this case, T1 = 1/2 and r=1/2, what we need to figure out is what n is, and in this case its simple. Its infinity! (1/2)^infitiy = 0, try to think about why this is true, you may want to refer back to jaime's post (right above this one).Now we can solve for what the sum would be.

S=(1/2)((1/2)^infinity-1)/((1/2)-1))
S= (1/2)(0-1)/((-1/2)
S= 1

In our case the terms of the series signified the distance of the trailer: 1/2 meant 1/2 of the trailer, then 1/4 of the trailer etc, so seeing as out answer is 1, the limit of Sybil's movement is 1 trailer.

May 17, 2007 at 12:10 PM
anto said...

I didn't proof read, just realized I have a typo in the second paragraph. I didn't mean to say serers but series.

May 17, 2007 at 12:13 PM

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