How can I rigorously prove that a finite set is countable?
A set is countable if there exists a bijective mapping from this set to that of natural numbers.
Please anyone help me to prove it. Thanks in advance.
How can I rigorously prove that a finite set is countable?
A set is countable if there exists a bijective mapping from this set to that of natural numbers.
Please anyone help me to prove it. Thanks in advance.
You will most likely want to appeal to the more rigorous definition of countability, namely that a set $S$ is countable if there is an injective function $f : S \to \mathbb{N}$. That is, you must show that every item in $S$ can be assigned to a unique natural number. Because $S$ is finite, this means that there are at most $k$ such elements in $S$. The rest of the "proof" is the trivial act of creating such an assignment for each element of $S$.