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Quandaries & Queries
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 Topic: infinities
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 How can other infinites can be larger than each other? 2009-02-17 From Justin:Hello again, I was just wondering even in the context of set theory, how can other infinites can be larger than each other, I thought infinity itself is the largest possible quantity? JustinAnswered by Victoria West and Robert Dawson. 0.999..., asymptotes and infinity 2004-12-17 From Mike:My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!!Answered by Claude Tardif and Harley Weston. Different infinities 2004-05-27 From Plober:How can I explain to a friend (in a bar, using as a pen and a paper napkin) that the integer's infinity is 'smaller' than the irrationals's one? The demo I tried was that you couldn't match the integers with the real numbers between 0 and 1 (that 0.xxxxx replacing the Nth number from a different one... that demo), but she used my argument >:| saying that you can add one to the integer's infinite, and the number I was creating was only one more... I can't think of any other way, and I KNOW the real's cardinality is greater than the integer's oneAnswered by Claude Tardif and Penny Nom.

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