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I'm not English native and I found these sentences in my math-textbook written in English

Let P denote the set of possible plaintexts.
Let K denote the set of possible keys.
Let C denote the set of ciphertexts.

But... what is the meaning of possible in this context?
What is a possible plaintext?
And Then, What is a impossible plaintext?

Asaf Karagila
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marinemorine
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  • Generally, the set of possible something or rather is the set of all relevant objects under some restriction. So given the situation, all plaintexts which satisfy your restriction are in $P$. For example, if Bob has no number '$0$' on his keyboard, the possible plaintexts are those using all numbers except $0$. The plaintext $101$ is impossible, as there would be no way for him to write it. – While I Am May 10 '21 at 12:39
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    @William If you could make that into an answer, it would help get this off of the unanswered list – Mark S. May 10 '21 at 12:41

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At Mark S.'s recommendation, I am posting this as an answer.

Often, the set of possible something or rather is the set of all relevant objects under some restriction. So given the situation, all plaintexts which satisfy your restriction are in P. For example, if Bob has no number '$0$' on his keyboard, the possible plaintexts are those using all numbers except $0$. The plaintext $101$ is impossible, as there would be no way for him to write it.

More generally, mathematicians have a concept of 'existence,' which just means there is no logical contradiction in an object satisfying certain properties. For example, we say that an even prime number exists, since $2$ certainly is both even and prime. Hence the set of possible objects are those which exist given a set of constraints. The set of all possible even prime numbers is just $\{2\}$.

While I Am
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