Question

how to word this. if we just look at the decimal portion of a number; 0.xxxxxx... ; can those be defined entotal by the natural numbers? or is there some combination of "xxxxx..." that is not included in the natural numbers?

Answer 1

Sorry I don't know

Answer 2

for example:

3.14159.... can be thought of as, 3 | 14159....

is the 14159.... create a natural number that does or does not exist?

Answer 3

Cantors diagonalization thrm makes no sense to me .....

Answer 4

.....abc | def .....
<-- countable uncountable -->

Answer 5

probably the decimal is countably infinite ..

Answer 6

cantor says it aint; which is why the set of Reals is uncountable

Answer 7

no ... i meant the set of real number between any two non equal interval in not countable.
but for particular real number ... the digits beyond decimal are countable.