Mixing
Basic explanation and examples on mute variables
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I would like to get from you some feedback regarding mute variables. Specifically, I would love to get an easy definition or description, one that I could convey to high school kids. I would also need some examples, accordingly, to illustrate.
One last thing, a little bit more technical. I would love to know in which way mute variables in mathematics relate to mute variables in lambda calculus, as I know it from Logic.
Bets regards and thanks in advance.
logic terminology education
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
asked Jul 28 at 17:16
Javier Arias
878617
add a comment |Â
up vote
2
down vote
favorite
I would like to get from you some feedback regarding mute variables. Specifically, I would love to get an easy definition or description, one that I could convey to high school kids. I would also need some examples, accordingly, to illustrate.
One last thing, a little bit more technical. I would love to know in which way mute variables in mathematics relate to mute variables in lambda calculus, as I know it from Logic.
Bets regards and thanks in advance.
logic terminology education
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
asked Jul 28 at 17:16
Javier Arias
878617
3
What do you mean by "mute variable" in mathematics?
– Noah Schweber
Jul 28 at 17:18
@NoahSchweber Maybe dummy variables??
– Lord Shark the Unknown
Jul 28 at 17:21
I mean variables which are local, so that they can be used several times for different goals without incurring in contradiction.
– Javier Arias
Jul 28 at 17:47
You may find "Structure and Interpretation of Classical Mechanics" interesting. In my experience, compared to programmers, mathematicians handle scoping poorly and mathematical notation is often extremely unclear about the scopes of things or even that some construct is a binding form at all. (Personally, I think this is a major factor in why so many find calculus difficult. It is one of the first subjects taught where scoping is used non-trivially, but it has some of the worst notation for it and educators don't seem inclined to dedicate the time to explicitly discussing scoping.)
– Derek Elkins
Jul 28 at 19:20
This is a very relevant comment, I think. Thanks. I am trained as a linguist to pay a lot of attention to the scope of binding....So that is probably the rationale behind my question...
– Javier Arias
Jul 28 at 20:56
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I would like to get from you some feedback regarding mute variables. Specifically, I would love to get an easy definition or description, one that I could convey to high school kids. I would also need some examples, accordingly, to illustrate.
One last thing, a little bit more technical. I would love to know in which way mute variables in mathematics relate to mute variables in lambda calculus, as I know it from Logic.
Bets regards and thanks in advance.
logic terminology education
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
asked Jul 28 at 17:16
Javier Arias
878617
I would like to get from you some feedback regarding mute variables. Specifically, I would love to get an easy definition or description, one that I could convey to high school kids. I would also need some examples, accordingly, to illustrate.
One last thing, a little bit more technical. I would love to know in which way mute variables in mathematics relate to mute variables in lambda calculus, as I know it from Logic.
Bets regards and thanks in advance.
logic terminology education
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
asked Jul 28 at 17:16
Javier Arias
878617
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
edited Jul 29 at 19:36
Mike Pierce
10.9k93574
10.9k93574
asked Jul 28 at 17:16
Javier Arias
878617
asked Jul 28 at 17:16
Javier Arias
878617
asked Jul 28 at 17:16
Javier Arias
878617
878617
3
What do you mean by "mute variable" in mathematics?
– Noah Schweber
Jul 28 at 17:18
@NoahSchweber Maybe dummy variables??
– Lord Shark the Unknown
Jul 28 at 17:21
I mean variables which are local, so that they can be used several times for different goals without incurring in contradiction.
– Javier Arias
Jul 28 at 17:47
You may find "Structure and Interpretation of Classical Mechanics" interesting. In my experience, compared to programmers, mathematicians handle scoping poorly and mathematical notation is often extremely unclear about the scopes of things or even that some construct is a binding form at all. (Personally, I think this is a major factor in why so many find calculus difficult. It is one of the first subjects taught where scoping is used non-trivially, but it has some of the worst notation for it and educators don't seem inclined to dedicate the time to explicitly discussing scoping.)
– Derek Elkins
Jul 28 at 19:20
This is a very relevant comment, I think. Thanks. I am trained as a linguist to pay a lot of attention to the scope of binding....So that is probably the rationale behind my question...
– Javier Arias
Jul 28 at 20:56
add a comment |Â
3
What do you mean by "mute variable" in mathematics?
– Noah Schweber
Jul 28 at 17:18
@NoahSchweber Maybe dummy variables??
– Lord Shark the Unknown
Jul 28 at 17:21
I mean variables which are local, so that they can be used several times for different goals without incurring in contradiction.
– Javier Arias
Jul 28 at 17:47
You may find "Structure and Interpretation of Classical Mechanics" interesting. In my experience, compared to programmers, mathematicians handle scoping poorly and mathematical notation is often extremely unclear about the scopes of things or even that some construct is a binding form at all. (Personally, I think this is a major factor in why so many find calculus difficult. It is one of the first subjects taught where scoping is used non-trivially, but it has some of the worst notation for it and educators don't seem inclined to dedicate the time to explicitly discussing scoping.)
– Derek Elkins
Jul 28 at 19:20
This is a very relevant comment, I think. Thanks. I am trained as a linguist to pay a lot of attention to the scope of binding....So that is probably the rationale behind my question...
– Javier Arias
Jul 28 at 20:56
3
3
What do you mean by "mute variable" in mathematics?
– Noah Schweber
Jul 28 at 17:18
What do you mean by "mute variable" in mathematics?
– Noah Schweber
Jul 28 at 17:18
@NoahSchweber Maybe dummy variables??
– Lord Shark the Unknown
Jul 28 at 17:21
@NoahSchweber Maybe dummy variables??
– Lord Shark the Unknown
Jul 28 at 17:21
I mean variables which are local, so that they can be used several times for different goals without incurring in contradiction.
– Javier Arias
Jul 28 at 17:47
I mean variables which are local, so that they can be used several times for different goals without incurring in contradiction.
– Javier Arias
Jul 28 at 17:47
You may find "Structure and Interpretation of Classical Mechanics" interesting. In my experience, compared to programmers, mathematicians handle scoping poorly and mathematical notation is often extremely unclear about the scopes of things or even that some construct is a binding form at all. (Personally, I think this is a major factor in why so many find calculus difficult. It is one of the first subjects taught where scoping is used non-trivially, but it has some of the worst notation for it and educators don't seem inclined to dedicate the time to explicitly discussing scoping.)
– Derek Elkins
Jul 28 at 19:20
You may find "Structure and Interpretation of Classical Mechanics" interesting. In my experience, compared to programmers, mathematicians handle scoping poorly and mathematical notation is often extremely unclear about the scopes of things or even that some construct is a binding form at all. (Personally, I think this is a major factor in why so many find calculus difficult. It is one of the first subjects taught where scoping is used non-trivially, but it has some of the worst notation for it and educators don't seem inclined to dedicate the time to explicitly discussing scoping.)
– Derek Elkins
Jul 28 at 19:20
This is a very relevant comment, I think. Thanks. I am trained as a linguist to pay a lot of attention to the scope of binding....So that is probably the rationale behind my question...
– Javier Arias
Jul 28 at 20:56
This is a very relevant comment, I think. Thanks. I am trained as a linguist to pay a lot of attention to the scope of binding....So that is probably the rationale behind my question...
– Javier Arias
Jul 28 at 20:56
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
You may think that a formula has an author and users. A formula can contain variables, that is, symbols that can be assigned values, very useful to parametrize. Such variables can be categorized by who, between the author and a user, is allowed to assign values.
$$f(x)=sum_i=1^10x^i$$
Here the author has conveniently made use of the parametrization feature of variables with the variable $i$. She bound $i$ iteratively to the integers in the range $1$ to $10$. So $i$ is a bound variable.
At the same time the author gave the users of her formula the possibility to use that formula parametrically. That is, a user is free to assign a value to $x$, it's a free variable, it is open bound. Then for the user, the bound variable $i$ is not usable. It's dummy, so to say, from the user perspective, or it does not claim to be assigned, it's thus mute.
Moreover, as you say in your comment you can reuse the name $i$ in the same formula to represent different dummy variables, with no name clashing.
EDIT:
Here the same name $n$ is used to name two different dummy variables:
$$f(x) = frac12a_0+sum_n=1^infty a_n cos (nx)+sum_n=1^infty b_n sin (nx)$$
where
beginalign
a_0 &=frac1piint_-pi^pi f(x)dx\
a_n &=frac1piint_-pi^pi f(x)cos(nx)dx\
b_n &=frac1piint_-pi^pi f(x)sin(nx)dx\
endalign
answered Jul 28 at 18:10
trying
4,0461722
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
A better example just added to the answer.
– trying
Jul 28 at 18:54
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
 |Â
show 6 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
You may think that a formula has an author and users. A formula can contain variables, that is, symbols that can be assigned values, very useful to parametrize. Such variables can be categorized by who, between the author and a user, is allowed to assign values.
$$f(x)=sum_i=1^10x^i$$
Here the author has conveniently made use of the parametrization feature of variables with the variable $i$. She bound $i$ iteratively to the integers in the range $1$ to $10$. So $i$ is a bound variable.
At the same time the author gave the users of her formula the possibility to use that formula parametrically. That is, a user is free to assign a value to $x$, it's a free variable, it is open bound. Then for the user, the bound variable $i$ is not usable. It's dummy, so to say, from the user perspective, or it does not claim to be assigned, it's thus mute.
Moreover, as you say in your comment you can reuse the name $i$ in the same formula to represent different dummy variables, with no name clashing.
EDIT:
Here the same name $n$ is used to name two different dummy variables:
$$f(x) = frac12a_0+sum_n=1^infty a_n cos (nx)+sum_n=1^infty b_n sin (nx)$$
where
beginalign
a_0 &=frac1piint_-pi^pi f(x)dx\
a_n &=frac1piint_-pi^pi f(x)cos(nx)dx\
b_n &=frac1piint_-pi^pi f(x)sin(nx)dx\
endalign
answered Jul 28 at 18:10
trying
4,0461722
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
A better example just added to the answer.
– trying
Jul 28 at 18:54
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
 |Â
show 6 more comments
up vote
1
down vote
accepted
You may think that a formula has an author and users. A formula can contain variables, that is, symbols that can be assigned values, very useful to parametrize. Such variables can be categorized by who, between the author and a user, is allowed to assign values.
$$f(x)=sum_i=1^10x^i$$
Here the author has conveniently made use of the parametrization feature of variables with the variable $i$. She bound $i$ iteratively to the integers in the range $1$ to $10$. So $i$ is a bound variable.
At the same time the author gave the users of her formula the possibility to use that formula parametrically. That is, a user is free to assign a value to $x$, it's a free variable, it is open bound. Then for the user, the bound variable $i$ is not usable. It's dummy, so to say, from the user perspective, or it does not claim to be assigned, it's thus mute.
Moreover, as you say in your comment you can reuse the name $i$ in the same formula to represent different dummy variables, with no name clashing.
EDIT:
Here the same name $n$ is used to name two different dummy variables:
$$f(x) = frac12a_0+sum_n=1^infty a_n cos (nx)+sum_n=1^infty b_n sin (nx)$$
where
beginalign
a_0 &=frac1piint_-pi^pi f(x)dx\
a_n &=frac1piint_-pi^pi f(x)cos(nx)dx\
b_n &=frac1piint_-pi^pi f(x)sin(nx)dx\
endalign
answered Jul 28 at 18:10
trying
4,0461722
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
A better example just added to the answer.
– trying
Jul 28 at 18:54
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
 |Â
show 6 more comments
up vote
1
down vote
accepted
up vote
1
down vote
accepted
You may think that a formula has an author and users. A formula can contain variables, that is, symbols that can be assigned values, very useful to parametrize. Such variables can be categorized by who, between the author and a user, is allowed to assign values.
$$f(x)=sum_i=1^10x^i$$
Here the author has conveniently made use of the parametrization feature of variables with the variable $i$. She bound $i$ iteratively to the integers in the range $1$ to $10$. So $i$ is a bound variable.
At the same time the author gave the users of her formula the possibility to use that formula parametrically. That is, a user is free to assign a value to $x$, it's a free variable, it is open bound. Then for the user, the bound variable $i$ is not usable. It's dummy, so to say, from the user perspective, or it does not claim to be assigned, it's thus mute.
Moreover, as you say in your comment you can reuse the name $i$ in the same formula to represent different dummy variables, with no name clashing.
EDIT:
Here the same name $n$ is used to name two different dummy variables:
$$f(x) = frac12a_0+sum_n=1^infty a_n cos (nx)+sum_n=1^infty b_n sin (nx)$$
where
beginalign
a_0 &=frac1piint_-pi^pi f(x)dx\
a_n &=frac1piint_-pi^pi f(x)cos(nx)dx\
b_n &=frac1piint_-pi^pi f(x)sin(nx)dx\
endalign
answered Jul 28 at 18:10
trying
4,0461722
You may think that a formula has an author and users. A formula can contain variables, that is, symbols that can be assigned values, very useful to parametrize. Such variables can be categorized by who, between the author and a user, is allowed to assign values.
$$f(x)=sum_i=1^10x^i$$
Here the author has conveniently made use of the parametrization feature of variables with the variable $i$. She bound $i$ iteratively to the integers in the range $1$ to $10$. So $i$ is a bound variable.
At the same time the author gave the users of her formula the possibility to use that formula parametrically. That is, a user is free to assign a value to $x$, it's a free variable, it is open bound. Then for the user, the bound variable $i$ is not usable. It's dummy, so to say, from the user perspective, or it does not claim to be assigned, it's thus mute.
Moreover, as you say in your comment you can reuse the name $i$ in the same formula to represent different dummy variables, with no name clashing.
EDIT:
Here the same name $n$ is used to name two different dummy variables:
$$f(x) = frac12a_0+sum_n=1^infty a_n cos (nx)+sum_n=1^infty b_n sin (nx)$$
where
beginalign
a_0 &=frac1piint_-pi^pi f(x)dx\
a_n &=frac1piint_-pi^pi f(x)cos(nx)dx\
b_n &=frac1piint_-pi^pi f(x)sin(nx)dx\
endalign
answered Jul 28 at 18:10
trying
4,0461722
edited Jul 28 at 18:53
answered Jul 28 at 18:10
trying
4,0461722
answered Jul 28 at 18:10
trying
4,0461722
answered Jul 28 at 18:10
trying
4,0461722
4,0461722
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
A better example just added to the answer.
– trying
Jul 28 at 18:54
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
 |Â
show 6 more comments
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
A better example just added to the answer.
– trying
Jul 28 at 18:54
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
could you provide an example in which a dummy variable appears several times in a formula, with different values each? Thanks
– Javier Arias
Jul 28 at 18:12
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
trivially $f(x)=left(sum_i=1^10x^iright)left(sum_i=1^10x^iright)$
– trying
Jul 28 at 18:26
A better example just added to the answer.
– trying
Jul 28 at 18:54
A better example just added to the answer.
– trying
Jul 28 at 18:54
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
so the proper name is dummy variable? I have read mute variable sometimes.....and also when dealing with Logic, Lamdba calculus, etc....If someone could clarify the relation of those dummy variables to lambda, I would be very grateful.
– Javier Arias
Jul 28 at 19:13
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
@JavierArias You should get out of the habit of thought that things have a single "proper" name. It simply doesn't reflect reality, especially when it comes to notation. I have also seen "mute variable" used, though my impression is "dummy variable" is more common. I dislike both and would prefer "bound variable", which is even more common, though it depends on the community.
– Derek Elkins
Jul 28 at 19:27
 |Â
show 6 more comments
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3
What do you mean by "mute variable" in mathematics?
– Noah Schweber
Jul 28 at 17:18
@NoahSchweber Maybe dummy variables??
– Lord Shark the Unknown
Jul 28 at 17:21
I mean variables which are local, so that they can be used several times for different goals without incurring in contradiction.
– Javier Arias
Jul 28 at 17:47
You may find "Structure and Interpretation of Classical Mechanics" interesting. In my experience, compared to programmers, mathematicians handle scoping poorly and mathematical notation is often extremely unclear about the scopes of things or even that some construct is a binding form at all. (Personally, I think this is a major factor in why so many find calculus difficult. It is one of the first subjects taught where scoping is used non-trivially, but it has some of the worst notation for it and educators don't seem inclined to dedicate the time to explicitly discussing scoping.)
– Derek Elkins
Jul 28 at 19:20
This is a very relevant comment, I think. Thanks. I am trained as a linguist to pay a lot of attention to the scope of binding....So that is probably the rationale behind my question...
– Javier Arias
Jul 28 at 20:56