Mixing
How can I notate the assignment of each variable in a tuple to a specific value?
$begingroup$
Assume I have a tuple of variables, i.e. $mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally correct way? Maybe using the $forall$ symbol?
notation
asked Jan 21 at 13:11
ChrisChris
1084
$endgroup$
add a comment |
$begingroup$
Assume I have a tuple of variables, i.e. $mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally correct way? Maybe using the $forall$ symbol?
notation
asked Jan 21 at 13:11
ChrisChris
1084
$endgroup$
1
$begingroup$
$x_1 = x_2 = ldots = c_n = c$?
$endgroup$
– Bermudes
Jan 21 at 13:14
add a comment |
$begingroup$
Assume I have a tuple of variables, i.e. $mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally correct way? Maybe using the $forall$ symbol?
notation
asked Jan 21 at 13:11
ChrisChris
1084
$endgroup$
Assume I have a tuple of variables, i.e. $mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally correct way? Maybe using the $forall$ symbol?
notation
notation
asked Jan 21 at 13:11
ChrisChris
1084
asked Jan 21 at 13:11
ChrisChris
1084
edited Jan 21 at 13:14
Chris
asked Jan 21 at 13:11
ChrisChris
1084
asked Jan 21 at 13:11
ChrisChris
1084
asked Jan 21 at 13:11
ChrisChris
1084
1084
1
$begingroup$
$x_1 = x_2 = ldots = c_n = c$?
$endgroup$
– Bermudes
Jan 21 at 13:14
add a comment |
1
$begingroup$
$x_1 = x_2 = ldots = c_n = c$?
$endgroup$
– Bermudes
Jan 21 at 13:14
1
1
$begingroup$
$x_1 = x_2 = ldots = c_n = c$?
$endgroup$
– Bermudes
Jan 21 at 13:14
$begingroup$
$x_1 = x_2 = ldots = c_n = c$?
$endgroup$
– Bermudes
Jan 21 at 13:14
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Why not just write $x_i=c$ for all $i$, or, as suggested above, $x_1=cdots=x_n=c$? You could also write $(x_1,ldots,x_n)=(c,ldots,c)$.
If you wanted to use notation alone, you could write
$$forall 1leq ileq n:x_i=c$$
or if the range is understood,
$$forall i:x_i=c$$
However it's a bit of a pet peeve of mine when people only use notation like this. Words are often more understandable. If you do use this, use it sparingly, unless you actually are writing formal strings for the purpose of studying them.
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
$endgroup$
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
2
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Why not just write $x_i=c$ for all $i$, or, as suggested above, $x_1=cdots=x_n=c$? You could also write $(x_1,ldots,x_n)=(c,ldots,c)$.
If you wanted to use notation alone, you could write
$$forall 1leq ileq n:x_i=c$$
or if the range is understood,
$$forall i:x_i=c$$
However it's a bit of a pet peeve of mine when people only use notation like this. Words are often more understandable. If you do use this, use it sparingly, unless you actually are writing formal strings for the purpose of studying them.
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
$endgroup$
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
2
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
add a comment |
$begingroup$
Why not just write $x_i=c$ for all $i$, or, as suggested above, $x_1=cdots=x_n=c$? You could also write $(x_1,ldots,x_n)=(c,ldots,c)$.
If you wanted to use notation alone, you could write
$$forall 1leq ileq n:x_i=c$$
or if the range is understood,
$$forall i:x_i=c$$
However it's a bit of a pet peeve of mine when people only use notation like this. Words are often more understandable. If you do use this, use it sparingly, unless you actually are writing formal strings for the purpose of studying them.
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
$endgroup$
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
2
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
add a comment |
$begingroup$
Why not just write $x_i=c$ for all $i$, or, as suggested above, $x_1=cdots=x_n=c$? You could also write $(x_1,ldots,x_n)=(c,ldots,c)$.
If you wanted to use notation alone, you could write
$$forall 1leq ileq n:x_i=c$$
or if the range is understood,
$$forall i:x_i=c$$
However it's a bit of a pet peeve of mine when people only use notation like this. Words are often more understandable. If you do use this, use it sparingly, unless you actually are writing formal strings for the purpose of studying them.
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
$endgroup$
Why not just write $x_i=c$ for all $i$, or, as suggested above, $x_1=cdots=x_n=c$? You could also write $(x_1,ldots,x_n)=(c,ldots,c)$.
If you wanted to use notation alone, you could write
$$forall 1leq ileq n:x_i=c$$
or if the range is understood,
$$forall i:x_i=c$$
However it's a bit of a pet peeve of mine when people only use notation like this. Words are often more understandable. If you do use this, use it sparingly, unless you actually are writing formal strings for the purpose of studying them.
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
edited Jan 21 at 13:19
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
answered Jan 21 at 13:14
Matt SamuelMatt Samuel
38.8k63769
38.8k63769
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
2
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
add a comment |
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
2
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
$begingroup$
True, I could do that, but I don't think its nice. I thought more about something like: $forall x_i in mathcal{T}: x_i = c$ but I don't know if that is correct formally.
$endgroup$
– Chris
Jan 21 at 13:15
2
2
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read.
$endgroup$
– Matt Samuel
Jan 21 at 13:16
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
@Chris I put in two examples of doing it the way you suggest.
$endgroup$
– Matt Samuel
Jan 21 at 13:20
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view?
$endgroup$
– Chris
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
$begingroup$
@Chris Yes. You could quantify over the set or over the index.
$endgroup$
– Matt Samuel
Jan 21 at 13:22
add a comment |
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$begingroup$
$x_1 = x_2 = ldots = c_n = c$?
$endgroup$
– Bermudes
Jan 21 at 13:14