Friday, September 16, 2011
Infinity+Infinity+Infinity
It seems Infinity is a bit slippery and just out of reach at ALL TIMES. It is bounded, unbounded, AND order matters? "The Rule of Infinity" is a concept that became a little less foggy(However, not at first!) for me when Professor Hamman proposed the infinite bus/hotel room scenario. The idea that infinity plus infinity (or even infinity + infinity + inifinity) really can be partially compartmentalized in a predictable way, can be accounted for and has value is astounding to me. I feel like I have started to grasp what the bounded aspects of infinity represent and how order plays a role and little about the unbounded possiblities it holds.
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ReplyDeleteThere was something similar to this that I thought of in class, but never got around to saying. Just as there is a way to combine a finite group of infinities into one, you can also break one infinity up into multiple others by skipping when you count. Say, for example you take one infinite set. You can then make one infinite set out of the even terms, and another out of the odd terms. This can be generalized to any finite number of infinite subsets. However, if you want to break up an infinite set into an infinite number of infinite subsets, this method wouldn't work, and you would need to count in some special order, like Cantor's diagonalization.
ReplyDeleteTracy, I def agree that infinity is a little slippery that we can't get a hang of what it is yet...or probably never, but it's so universal that it's always around us. The bounded and the unbounded part that you mentioned in your post made me think that maybe there are a certain amount of finite that you can take out from a group of infinite, while at the same time, you can take out a group of infinite from a group of finite. For instance, most of us think that the world is a finite matter with a certain amount of elements in it, yet we are here talking about infinity in a world that is finite.
ReplyDeleteHi Tracy,
ReplyDeleteI don't know whether to say infinite is accountable or not especially when I consider the fact that the one to one correspondence example made a perfect sense of what infinite was all about. The numbers corresponded so well and no matter how you take one out and add another it doesn't change the process. At one time it feel like you can account for them but as you add more it doesn't stop so you cannot account for them either. If you take infinite out of infinite you get the same infinity. Cantor was trying to use rational numbers to point out that "the actual infinite means to deny the existence of irrational numbers, for such numbers has infinite decimal expansion...( To infinite and Beyond, p55). This totally makes sense in a way because you can never know the exact value of the end of irrational numbers when you put them on your calculator. Like Tracy said it's kind of foggy when you think about it in other ways but mathematically it makes sense somehow.
Yaa
Yaa, nice citation. lol it's taken me so long to think of a response to all these posts. I'm still absorbing last class! the idea really blew my mind that in the infinite hotel you could keep adding more. What really got me thinking though was how there was no last person. so that means that zig zag is endless as well. I'm also a bit discouraged.. like why keep counting if you're never going to reach an end? it's kinda scary to think about. It just keeps going. The hotel example though, helped me somewhat grasp my mind around there being some type of order. I always thought that though. For example, when I think of space I don't believe anything is random. I once heard that if our planet were like two inches (could be wrong about the measurement) closer to the sun we'd all burn. That's order! But to think that this order is predictable (not referring to planetary alignment, but this infinite vastness) through numbers is really interesting to think about, Its not just a dark "endless ness," it's like a hotel that still has room for more. So space is forever expanding? This leads me to believe Infinity is incomprehensible and yet understandable.
ReplyDeleteI understand that I can't comprehend what it means for something to forever expand because I will always search for an end, but I can understand that there is an order in this infinite expansion that makes the idea of the infinite comprehensible. I just went in a circle, but this is what I have concluded about infinity from the second class.
ReplyDeleteIn terms of the hotel example,I was kind of frustrated when we came to the point nobody knows where the last person would go. In other words, there's no last person. Apparently, my imaginary is limited, i can't imagine an infinite hotel. It's just not real to me.
ReplyDeleteHowever, i agree with Tracy that i have learned how order plays a role in it
The idea that infinity is irreducible (as we explored mathematically last class) really got me thinking on other levels as well. My health teacher Professor Meinier always said, "Nature abhors a vacuum." if someone digs a hole, grass grows back and eventually and the hole will fill back up. water and electricity take the path of least resistance to "fill up" or "even out" the gap. Seems with the earth, this oh so finite earth has traits of infinity all around. Embedded in it's very laws of nature. Maybe this is just a weird way of defining energy and matter being infinitely conserved. But it's as if the earth itself has a grasp on this elusive subject: You take something away from it---even itself (ie gaps in tectonic plates) then it fills its own void (ie mountains form) without the upset of human industrial development, I wonder if this finite earth could teach us about infinity.
ReplyDeleteIn the philosophical realm, I wonder if it applies: If a child grows up in a household with no love or justice does the child make it (albeith possibly subconciously) their motive to find these things elsewhere in life later on? To fill a void...
wups this is long...
is infinity complete?