4 ms·

> You can keep on dividing forever, so every line has an infinite amount of parts. But how long are those parts? If they're anything greater than zero, then the

> You can keep on dividing forever, so every line has an infinite amount of parts. But how long are those parts? If they're anything greater than zero, then the line would seem to be infinitely long. And if they're zero, well, then no matter how many parts there are, the length of the line would still be zero. Sigh. There is no paradox here, except to those who fundamentally fail to grasp the concept of infinity. Infinity is not a number. Multiplying length by infinity is a type error. This is nonsensical, not paradoxical. I don't buy the hand-waving argument that this somewhat arcane debate had so much impact on the course of history. Obviously nobody can prove it true or false, because the alternative outcome is unknowable. I'm inclined to ignore unfalsifiable speculation.

goldenkey 12y ago
Right. Infinite is a procedure that can be taken to be a value (with the right context.)
- anaphor 12y ago
  It annoys me when people try to argue that (0.99...) != 1 because "infinity goes on forever, it's not a number!" though, without understanding the difference between a representation of a number and the number itself.
  - GregBuchholz 12y ago
    Of course that argument only applies when talking about the standard real number system. http://arxiv.org/pdf/1007.3018.pdf?origin=publication_detail http://arxiv.org/pdf/1007.3018.pdf?origin=publication_detail http://arxiv.org/pdf/0811.0164.pdf http://arxiv.org/pdf/0811.0164.pdf ...of course you can make a pretty good case that uncountable, uncomputable, unnameable, unknowable "real" numbers don't exist. http://arxiv.org/abs/math/0404335 http://arxiv.org/abs/math/0404335 ...(the impatient should jump to chapter 5). And maybe also: http://web.maths.unsw.edu.au/~norman/views2.htm http://web.maths.unsw.edu.au/~norman/views2.htm
GregBuchholz 12y ago
>Infinity is not a number. http://en.wikipedia.org/wiki/Hyperreal_number http://en.wikipedia.org/wiki/Hyperreal_number http://en.wikipedia.org/wiki/Surreal_number http://en.wikipedia.org/wiki/Surreal_number

goldenkey 12y ago

Right. Infinite is a procedure that can be taken to be a value (with the right context.)

anaphor 12y ago
It annoys me when people try to argue that (0.99...) != 1 because "infinity goes on forever, it's not a number!" though, without understanding the difference between a representation of a number and the number itself.
- GregBuchholz 12y ago
  Of course that argument only applies when talking about the standard real number system. http://arxiv.org/pdf/1007.3018.pdf?origin=publication_detail http://arxiv.org/pdf/1007.3018.pdf?origin=publication_detail http://arxiv.org/pdf/0811.0164.pdf http://arxiv.org/pdf/0811.0164.pdf ...of course you can make a pretty good case that uncountable, uncomputable, unnameable, unknowable "real" numbers don't exist. http://arxiv.org/abs/math/0404335 http://arxiv.org/abs/math/0404335 ...(the impatient should jump to chapter 5). And maybe also: http://web.maths.unsw.edu.au/~norman/views2.htm http://web.maths.unsw.edu.au/~norman/views2.htm

GregBuchholz 12y ago

>Infinity is not a number. http://en.wikipedia.org/wiki/Hyperreal_number http://en.wikipedia.org/wiki/Hyperreal_number http://en.wikipedia.org/wiki/Surreal_number http://en.wikipedia.org/wiki/Surreal_number