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{A,B,C} is of greater cardinality than {A,B}. However, the argument that "a rule works for finite numbers, so it must work for infinite numbers" is clearly fal
by pcmonk 10y ago
{A,B,C} is of greater cardinality than {A,B}. However, the argument that "a rule works for finite numbers, so it must work for infinite numbers" is clearly false.
For a your mapping, see: http://math.stackexchange.com/questions/512397/is-there-a-simple-constructive-1-1-mapping-between-the-reals-and-the-irrationa http://math.stackexchange.com/questions/512397/is-there-a-si...
- Retric 10y agoThe distance between 0 and 1 is smaller than the distance between 0 and 2. The number of points between 0 and 1 is larger than the number of rational numbers.
- pcmonk 10y ago> The distance between 0 and 1 is smaller than the distance between 0 and 2. This is correct. However, the number of real-valued points between 0 and 1 is the same as the number of real-valued points between 0 and 2. > The number of points between 0 and 1 is larger than the number of rational numbers. This is also true because there are uncountably many real-valued points between 0 and 1 and countably many rational numbers.