2007-07-04 06:22:25 · 5 answers · asked by (:P) 6 in Science & Mathematics ➔ Mathematics
Isn't it possible that since infinity can exist between boundaries, that the boundaries actually define the end of that set of numbers and therefore it is merely a measure of our own incapabilities?
2007-07-06 06:48:37 · update #1
Infinity is not a real number. This is just a representation that there are so many elements (without end) or that there are uncountably many elements.
In the interval notation, infinity means that you extend to the left or right indefinitely.
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2007-07-04 06:31:44 · answer #1 · answered by Alam Ko Iyan 7 · 0⤊ 0⤋
What do you mean by real? A set can have BOUNDARIES and still have an infinite number of elements. There are MANY kinds of infinity. Denumerable infinities can be put in 1 to 1 correspondance with the natural numbers (1, 2, 3, ....); nondenumerable infinities, such as the number of real numbers, cannot. Look up Cantor and Infinity on wikipedia. Half a century ago Lillian Lieber had an excellent book on infinity. Made it clear enough why Cantor went crazy.
2007-07-04 13:30:07 · answer #2 · answered by Philo 7 · 0⤊ 0⤋
What you've shown is that an infinite number of points can be fit into a finite interval. I don't know if that makes infinity any more or less "real". It's a concrete example of an infinite set, that much we can say.
2007-07-04 13:37:59 · answer #3 · answered by TFV 5 · 0⤊ 0⤋
Cut the interval between the two integers in half. Now cut that interval in half. Continue till you reach a number that can't be reduced.
2007-07-04 13:32:59 · answer #4 · answered by GeekCreole 4 · 0⤊ 0⤋
It's not really ended is it? There's still an infinite amount of numbers in between. So it is real ?
2007-07-04 13:30:31 · answer #5 · answered by koutetsu12 3 · 0⤊ 0⤋