Thoughts on Infinity
Date: 7/19/96 at 3:39:8 From: Anonymous Subject: Thoughts on Infinity Hello Docs! I was just reading through your helpful advice when I came across a question about subdivision of numbers and infinity. Sydney was commenting on how one infinity could be larger than another. I was wondering, since infinity is never-ending (so I think), wouldn't it be better to say that one infinity can be *denser* than another? Maybe I'm wrong, but its an idea. BTW, thanks for this page; it's really helpful, especially to somebody like me who struggles in math. Michelle Seattle, WA
Date: 7/23/96 at 14:45:17 From: Doctor Erich Subject: Re: Thoughts on Infinity Michelle, Thinking of one infinity as denser than another infinity is actually a great geometric way to visualize the difference between kinds of infinities. There are two basic kinds of infinities. One type is called countable, which basically means you can "number" the things you are counting. For example, if you had a bunch of t-shirts and wrote the numbers 1, 2, 3, 4, .... on them you would have a countably infinite number of t-shirts. So you can think of the natural numbers(numbers like 1,2,3,4,5,...) as countably infinite. The other type of infinity is uncountable (mathematicians sure come up with creative names...huh?). Uncountable means there are so many you can't "number" them. This is where infinity starts to get strange, but an example of something that is uncountably infinite is something like all the real numbers (numbers like 2.34.. and the square root of 2). In fact, there are more decimal numbers between 0 and 1 than there are natural numbers(1,2,3,4,...)! Your density idea is a good idea to picture different infinities, although my longwinded explanation may have been a lot more than you wanted. Anyway, keep thinking about math...if you want more information about infinity or anything else, feel free to write again! -Doctor Erich, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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