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Hey,Quote from: Colin Michael on June 06, 2009, 10:32:44 PMInfinity x X or Y is still infinity. I'd say that's an equality.Even when fudging the math and considering the idea of infinity in equations, the equation "infinity = infinity" is not always true. There are different orders of infinity that are not "equal" to each other. The way it was explained to me was that if hotel A has one floor and an infinite number of rooms on each floor and hotel B has an infinite number of floors and an infinite number of rooms on each floor then both hotels have an infinite number of rooms but hotel B has far more rooms than hotel A.Tschow,Tim "Sir Nobody" Maly
Infinity x X or Y is still infinity. I'd say that's an equality.
Another example of an uncountably infinite set is the Cantor set, K. This is obtained by deleting the middle third (1/3, 2/3) from [0,1]. Then, you delete the middle third from the segments [0,1/3) and (2/3,1]. Repeat this process ad infinitum, and the dust of points that remain is K. K is uncountably infinite for reasons that are beyond the scope of this post. :-)
Quote from: Egyptian on June 07, 2009, 01:52:21 PMAnother example of an uncountably infinite set is the Cantor set, K. This is obtained by deleting the middle third (1/3, 2/3) from [0,1]. Then, you delete the middle third from the segments [0,1/3) and (2/3,1]. Repeat this process ad infinitum, and the dust of points that remain is K. K is uncountably infinite for reasons that are beyond the scope of this post. :-)This is Chaos!
What I love about K is that it "seems" infinitely "less" than [0,1] yet is itself uncountably infinite!
I think what you're trying to get at here is "countably infinite" versus "uncountably infinite."
I'm kind of confused and lost with all of this.
Quote from: Colin Michael on June 07, 2009, 03:19:47 PMI'm kind of confused and lost with all of this.Your confused by big numbers and I'm confused by big words. I say we're even.
The uncountability of the real numbers never sat well with me.