All Questions
Tagged with uncountability counting
3 questions
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Is the set of all strings over $\Sigma$ countably infinite or not?
Let $\Sigma$ be an alphabet. Is the set of all strings over $\Sigma$ (i.e. $\Sigma^*$) countably infinite or uncountably infinite?
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What are the definitions of countable and measurable colourings of a graph?
In this paper, the author discusses colourings of the plane, or in other words, of the underlying graph. I suppose a finite colouring is a colouring using at most $k$ colours for some natural number $...
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How is the set of functions from ${\{a,b\}}$ to $N$ countable?
Assume a set of functions from ${\{a,b\}}$ to $N$
Where $N$ is the set of Natural numbers.
Let us assume that the size of $N$ is $n$.
i.e $|N|=n$
The first element $a$ have $n$ choices for mapping....
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