Question

how can an infinite set be countable or uncountable?

Answer 1

depends on whether you can count them or not

Answer 2

Well said @satellite73

Answer 3

every element in a countable infinite set can be mapped to the positive integers

Answer 4

uncountable infinite can not be mapped to the positive integers

Answer 5

definition of uncountable and example?

Answer 6

so if it cannot be indexed with natural numbers, it is deemed to be uncountable?

Answer 7

yes

Answer 8

an uncountable infinite set is one in which every element of the set can not be mapped to the positive integers. An example is the real numbers

Answer 9

it said to be countable if you can find a bijection between the infinite set and natural numbers
or if you know you can list them all basically

like you can try to list all the elements in (0,1)

we could keep going
but there will always be a number you could say that is not on the that list

the interval (0,1) is therefore not countable
because there is bijection between the naturals and (0,1)