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I’m new to formal language and searching for the solution for the following task:

$\Sigma$ is an alphabet with $\lvert \Sigma\rvert = 5$ and $k \in \mathbb{N}_0$.

I’m searching for $\lvert \Sigma^k\rvert$.

Willie Wong
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LaPhi
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  • This might help: http://math.stackexchange.com/questions/32247/a-question-on-notation-for-function-spaces/32251#32251 – joriki Apr 11 '11 at 08:00
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    $\Sigma^k$ is the set of $k$-letter words on the letters of $\Sigma$. You want to know how many of those there are. Hence @joriki's suggestion. – lhf Apr 11 '11 at 11:58

2 Answers2

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Thank you.

$\Sigma^k$ is the set of k-letter words on the letters of Σ. You want to know how many of those there are.

So, therefor the answer is {amount_of_letters}$^5$ ?

For example: {0,1} ... 2$^5$ words possible? {a,b,c} ... 3$^5$ words possible? and so on...

jensen
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    Yes. Think of a list $\Box\Box\Box\Box\Box$ and for each $\Box$ you can make $|\Sigma|$ distinct choices. So if you have $5$ boxes, there are $|\Sigma|^5$ possibilities. – t.b. Apr 11 '11 at 12:42
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proposal for solution:

k's are elements of natural number, including zero.

-> $\Sigma$'s cardinality is five. so $\Sigma^5$ = {01234} or {45678}

What I didn't understand: No word's parts are given, so how can I answer this question without knowing, what is part of the language.

What I can say is, $\Sigma^5$ has five-digit words like {abcde} or {01234}...

However, i doubt, that this is the right solution...

Best regards, jensen

jensen
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