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| Acmlm's Board - I3 Archive - - Posts by Nayno |
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Nayno Newcomer               Since: 12-15-05 Last post: 6337 days Last view: 6337 days |
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| There are multiple sizes of infinity; That means that one infinity can be larger than another, possibly infinitely larger. We know this because between any two points on the number line, say, 0 and 1, there is an infinite number of rational numbers. However, there is also an infinite number of irrational numbers (like pi or the square root of two)! There are, in fact, more irrational numbers than rational numbers, but there is an infinite number of each!
Why are there more irrational numbers? When you find the area underneath of a function using an integral, all of the area corresponds to irrational x-values and none of it corresponds to rational x-values. Think about it. The area underneath a function at some x-value is really just a line segment... it has zero area. Somehow, by adding together an infinite number of zero-area line segments, we find a definite area that is greater than zero! Where does all of the area come from? Irrational x-values. When you think about it, this means that Z may not be rational infinity, but irrational infinity. The area underneath the function = irrational infinity * the area of a line segment, or A = Z * 0. So while 0 * infinity does equal zero, it also can equal some constant depending on the properties of the infinity and the zero involved. Of course, I am not a math professor, but I do know a little bit about stuff like this. |
| Acmlm's Board - I3 Archive - - Posts by Nayno |
