The length of the sequence concatenated two sequences
$begingroup$
Let $alpha$ be a finite sequence, and $|alpha|$ be the length of $alpha$.
Let $alpha_1, alpha_2$ be two finite sequences. Prove that $|alpha_1 alpha_2| = |alpha_1 |+|alpha_2|$. Where $alpha_1 alpha_2$ is just the concatenation of the sequences $alpha_1$ and $alpha_2$.
This looks very obvious. But I do not know what to do if I want to deal with it more precisely.
logic propositional-calculus foundations
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
$endgroup$
add a comment |
$begingroup$
Let $alpha$ be a finite sequence, and $|alpha|$ be the length of $alpha$.
Let $alpha_1, alpha_2$ be two finite sequences. Prove that $|alpha_1 alpha_2| = |alpha_1 |+|alpha_2|$. Where $alpha_1 alpha_2$ is just the concatenation of the sequences $alpha_1$ and $alpha_2$.
This looks very obvious. But I do not know what to do if I want to deal with it more precisely.
logic propositional-calculus foundations
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
$endgroup$
$begingroup$
Do you mean sequence or set?
$endgroup$
– TheD0ubleT
Dec 5 '18 at 11:26
$begingroup$
@TheD0ubleT $alpha, alpha_1, alpha_2$ are all sequences.
$endgroup$
– amoogae
Dec 5 '18 at 11:28
2
$begingroup$
If you want to do this very formally, then we should start by asking what is your formal definition of sequence and concatenation. Then I suspect that your definition of concatenation will already contain the answer.
$endgroup$
– Michal Adamaszek
Dec 5 '18 at 12:17
$begingroup$
Thanks @MichalAdamaszek !!
$endgroup$
– amoogae
Dec 5 '18 at 12:33
add a comment |
$begingroup$
Let $alpha$ be a finite sequence, and $|alpha|$ be the length of $alpha$.
Let $alpha_1, alpha_2$ be two finite sequences. Prove that $|alpha_1 alpha_2| = |alpha_1 |+|alpha_2|$. Where $alpha_1 alpha_2$ is just the concatenation of the sequences $alpha_1$ and $alpha_2$.
This looks very obvious. But I do not know what to do if I want to deal with it more precisely.
logic propositional-calculus foundations
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
$endgroup$
Let $alpha$ be a finite sequence, and $|alpha|$ be the length of $alpha$.
Let $alpha_1, alpha_2$ be two finite sequences. Prove that $|alpha_1 alpha_2| = |alpha_1 |+|alpha_2|$. Where $alpha_1 alpha_2$ is just the concatenation of the sequences $alpha_1$ and $alpha_2$.
This looks very obvious. But I do not know what to do if I want to deal with it more precisely.
logic propositional-calculus foundations
logic propositional-calculus foundations
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
edited Dec 5 '18 at 12:35
Andrés E. Caicedo
65.5k8159250
65.5k8159250
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
asked Dec 5 '18 at 11:23
amoogaeamoogae
487
487
$begingroup$
Do you mean sequence or set?
$endgroup$
– TheD0ubleT
Dec 5 '18 at 11:26
$begingroup$
@TheD0ubleT $alpha, alpha_1, alpha_2$ are all sequences.
$endgroup$
– amoogae
Dec 5 '18 at 11:28
2
$begingroup$
If you want to do this very formally, then we should start by asking what is your formal definition of sequence and concatenation. Then I suspect that your definition of concatenation will already contain the answer.
$endgroup$
– Michal Adamaszek
Dec 5 '18 at 12:17
$begingroup$
Thanks @MichalAdamaszek !!
$endgroup$
– amoogae
Dec 5 '18 at 12:33
add a comment |
$begingroup$
Do you mean sequence or set?
$endgroup$
– TheD0ubleT
Dec 5 '18 at 11:26
$begingroup$
@TheD0ubleT $alpha, alpha_1, alpha_2$ are all sequences.
$endgroup$
– amoogae
Dec 5 '18 at 11:28
2
$begingroup$
If you want to do this very formally, then we should start by asking what is your formal definition of sequence and concatenation. Then I suspect that your definition of concatenation will already contain the answer.
$endgroup$
– Michal Adamaszek
Dec 5 '18 at 12:17
$begingroup$
Thanks @MichalAdamaszek !!
$endgroup$
– amoogae
Dec 5 '18 at 12:33
$begingroup$
Do you mean sequence or set?
$endgroup$
– TheD0ubleT
Dec 5 '18 at 11:26
$begingroup$
Do you mean sequence or set?
$endgroup$
– TheD0ubleT
Dec 5 '18 at 11:26
$begingroup$
@TheD0ubleT $alpha, alpha_1, alpha_2$ are all sequences.
$endgroup$
– amoogae
Dec 5 '18 at 11:28
$begingroup$
@TheD0ubleT $alpha, alpha_1, alpha_2$ are all sequences.
$endgroup$
– amoogae
Dec 5 '18 at 11:28
2
2
$begingroup$
If you want to do this very formally, then we should start by asking what is your formal definition of sequence and concatenation. Then I suspect that your definition of concatenation will already contain the answer.
$endgroup$
– Michal Adamaszek
Dec 5 '18 at 12:17
$begingroup$
If you want to do this very formally, then we should start by asking what is your formal definition of sequence and concatenation. Then I suspect that your definition of concatenation will already contain the answer.
$endgroup$
– Michal Adamaszek
Dec 5 '18 at 12:17
$begingroup$
Thanks @MichalAdamaszek !!
$endgroup$
– amoogae
Dec 5 '18 at 12:33
$begingroup$
Thanks @MichalAdamaszek !!
$endgroup$
– amoogae
Dec 5 '18 at 12:33
add a comment |
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$begingroup$
Do you mean sequence or set?
$endgroup$
– TheD0ubleT
Dec 5 '18 at 11:26
$begingroup$
@TheD0ubleT $alpha, alpha_1, alpha_2$ are all sequences.
$endgroup$
– amoogae
Dec 5 '18 at 11:28
2
$begingroup$
If you want to do this very formally, then we should start by asking what is your formal definition of sequence and concatenation. Then I suspect that your definition of concatenation will already contain the answer.
$endgroup$
– Michal Adamaszek
Dec 5 '18 at 12:17
$begingroup$
Thanks @MichalAdamaszek !!
$endgroup$
– amoogae
Dec 5 '18 at 12:33