• Aug 13th 2011, 03:57 PM
chuckg1982
I'm sure there is a name for this paradox, but I haven't studied set theory enough to know what it's called. Can someone please help resolve this?

Let N = the set of the natural numbers, and let D = the set of natural odd numbers.

N and D have equal cardinalities, and yet N is unequal to D. This is not a problem, for two sets can have similar cardinalities while maintaining their uniqueness.

The problem, for me anyway, is this: N and D are both infinite sets, and N is a proper superset of D. Thus, shouldn't the cardinality of N be greater than that of D?

Shouldn't a set always have a cardinality greater than that of its proper subset?
• Aug 13th 2011, 04:08 PM
Plato
There are just as many real numbers in $(0,1)$ as there are on the whole number line.