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A comment on What are the 'real numbers', really?. Parent comment

Re:What are the 'real numbers', really? by Someone on Thursday December 26, 2013 @03:08PM (#6967789)
"But if points have zero extension then even an infinity of them cannot sum to anything greater than zero."

Infinities are weird; anybody who wants to learn math has to accept that. 0.99999… does equal 1, there are as many even numbers as integers, etc. these things are 'true' not because they make sense initially, but because they make the most sense of all the other things we have thought of so far. Similarly, a set of Aleph-0 points can completely cover a line.

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Re:What are the 'real numbers', really? by mcguire on Thursday December 26, 2013 @05:49PM (#6968490)
"a set of Aleph-0 points can completely cover a line"

Aleph_0 is the cardinality of the integers. I don't think that'll cover a line. For that, you need the cardinality of the reals, C, which may or may not be Aleph_1.

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Re:What are the 'real numbers', really? by Someone on Thursday December 26, 2013 @07:26PM (#6968800)
OOPS. Thanks
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Re:What are the 'real numbers', really? by mcguire on Friday December 27, 2013 @12:06PM (#6971452)
Infinities are weird.
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