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

Germann

An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?

studiot

How does the set get to be infinite if there are only a finite number of members available?

1 person

AplanisTophet

No, because the set of hereditarily finite sets is countable.

1 person

Maschke

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.

1 person