An infinite set of finite sequences of combinations of a finite set of elements

Mar 2019
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Belarus
An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?
 
Jun 2015
915
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England
How does the set get to be infinite if there are only a finite number of members available?
 
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Aug 2012
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An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?
Say the finite set of elements has cardinality $n$.

There are $n$ distinct sequences of length 1.

There are $n^2$ sequences of length 2.

In general there are $n^k$ distinct sequences of length $k$.

The union of countably many finite sets is countable.
 
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