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michonamona
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Countable sets | If k:A-->N is 1-to-1, then A is...
Suppose we found a 1-to-1 function k that maps the set A to the set N, where N is the set of natural numbers. What can we say about the set A?
The answer is 'A is at most countable.' I understand this. But my question is, is it also possible for A to be finite, as well as infinite? i.e. its possible for A to be either
{a1, a2, a3}
or
{a1, a2, a3, a4, a5,...}
all the way to infinity.
Thanks,
M
Homework Statement
Suppose we found a 1-to-1 function k that maps the set A to the set N, where N is the set of natural numbers. What can we say about the set A?
Homework Equations
The Attempt at a Solution
The answer is 'A is at most countable.' I understand this. But my question is, is it also possible for A to be finite, as well as infinite? i.e. its possible for A to be either
{a1, a2, a3}
or
{a1, a2, a3, a4, a5,...}
all the way to infinity.
Thanks,
M