Mathematical language : how to explain the difference between “$x$ as an unknown” and “$x$ as a variable”? Unknown versus variable?Meaning of an EquationHigh school math definition of a variable: the first step from the concrete into the abstract…How to determine the operation(s) needed to obtain same value for variable in two formulas?How to formalize the notion of “context” and “arbitrary”? (In terms of “data types”?)Definition: what is the difference between generating a random variable versus generating a random number?Does “$lnot P$” mean “$P$ is false”? Or not? ( syntax versus semantics)
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Mathematical language : how to explain the difference between “$x$ as an unknown” and “$x$ as a variable”? Unknown versus variable?
Meaning of an EquationHigh school math definition of a variable: the first step from the concrete into the abstract…How to determine the operation(s) needed to obtain same value for variable in two formulas?How to formalize the notion of “context” and “arbitrary”? (In terms of “data types”?)Definition: what is the difference between generating a random variable versus generating a random number?Does “$lnot P$” mean “$P$ is false”? Or not? ( syntax versus semantics)
$begingroup$
How to explain precisely the distinction between "using the letter $x$ as an unknown" and "using the letter $x$ as a variable"?
Is it a syntactic difference? a semantic one?
is the difference pragmatic in nature ( relative to the intentions of the person that uses the symbol : "I want to find the value of $x$")?
Can I explain it in the following way :
$x$ is an unknown iff $x$ appears in a conditional equation
$x$ is a variable otherwise ( identity, defining formula of a function, etc?)
In a book ( Mathématiques de A à Z, Georges Alain , 1999) I read : " A variable is a number to which one can attribute any value one wants. An unknown is a number the possible values of which we are looking for. The oppositite of " variable" is " constant" , the opposite of " unknown" is " given").
In case this distinction would be outdated or out of use, what was the traditional explanation of this distinction?
algebra-precalculus terminology definition formal-languages
edited 3 mins ago
Asaf Karagila♦
311k33445777
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
$endgroup$
add a comment |
$begingroup$
How to explain precisely the distinction between "using the letter $x$ as an unknown" and "using the letter $x$ as a variable"?
Is it a syntactic difference? a semantic one?
is the difference pragmatic in nature ( relative to the intentions of the person that uses the symbol : "I want to find the value of $x$")?
Can I explain it in the following way :
$x$ is an unknown iff $x$ appears in a conditional equation
$x$ is a variable otherwise ( identity, defining formula of a function, etc?)
In a book ( Mathématiques de A à Z, Georges Alain , 1999) I read : " A variable is a number to which one can attribute any value one wants. An unknown is a number the possible values of which we are looking for. The oppositite of " variable" is " constant" , the opposite of " unknown" is " given").
In case this distinction would be outdated or out of use, what was the traditional explanation of this distinction?
algebra-precalculus terminology definition formal-languages
edited 3 mins ago
Asaf Karagila♦
311k33445777
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
$endgroup$
2
$begingroup$
It depends on the context. I would call $x$ a variable in both cases and eventually "unknown" if it is apparant that we aim to know which values it can take. Btw, there is also a distinction between free and bound variables. In the expression $int_0^x f(u)du$ variable $x$ is free and variable $u$ is bound.
$endgroup$
– drhab
8 hours ago
$begingroup$
"unknown" sounds obsolete and unclear. The line equation in the plane $y=x$, here $x,y$ are variables, but the line equation $x=1$, is here $x$ a variable or an unknown? Personally, I use "variable" in all cases.
$endgroup$
– A.Γ.
7 hours ago
add a comment |
$begingroup$
How to explain precisely the distinction between "using the letter $x$ as an unknown" and "using the letter $x$ as a variable"?
Is it a syntactic difference? a semantic one?
is the difference pragmatic in nature ( relative to the intentions of the person that uses the symbol : "I want to find the value of $x$")?
Can I explain it in the following way :
$x$ is an unknown iff $x$ appears in a conditional equation
$x$ is a variable otherwise ( identity, defining formula of a function, etc?)
In a book ( Mathématiques de A à Z, Georges Alain , 1999) I read : " A variable is a number to which one can attribute any value one wants. An unknown is a number the possible values of which we are looking for. The oppositite of " variable" is " constant" , the opposite of " unknown" is " given").
In case this distinction would be outdated or out of use, what was the traditional explanation of this distinction?
algebra-precalculus terminology definition formal-languages
edited 3 mins ago
Asaf Karagila♦
311k33445777
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
$endgroup$
How to explain precisely the distinction between "using the letter $x$ as an unknown" and "using the letter $x$ as a variable"?
Is it a syntactic difference? a semantic one?
is the difference pragmatic in nature ( relative to the intentions of the person that uses the symbol : "I want to find the value of $x$")?
Can I explain it in the following way :
$x$ is an unknown iff $x$ appears in a conditional equation
$x$ is a variable otherwise ( identity, defining formula of a function, etc?)
In a book ( Mathématiques de A à Z, Georges Alain , 1999) I read : " A variable is a number to which one can attribute any value one wants. An unknown is a number the possible values of which we are looking for. The oppositite of " variable" is " constant" , the opposite of " unknown" is " given").
In case this distinction would be outdated or out of use, what was the traditional explanation of this distinction?
algebra-precalculus terminology definition formal-languages
algebra-precalculus terminology definition formal-languages
edited 3 mins ago
Asaf Karagila♦
311k33445777
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
edited 3 mins ago
Asaf Karagila♦
311k33445777
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
edited 3 mins ago
Asaf Karagila♦
311k33445777
edited 3 mins ago
Asaf Karagila♦
311k33445777
edited 3 mins ago
Asaf Karagila♦
311k33445777
311k33445777
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
asked 8 hours ago
Ray LittleRockRay LittleRock
39910
39910
2
$begingroup$
It depends on the context. I would call $x$ a variable in both cases and eventually "unknown" if it is apparant that we aim to know which values it can take. Btw, there is also a distinction between free and bound variables. In the expression $int_0^x f(u)du$ variable $x$ is free and variable $u$ is bound.
$endgroup$
– drhab
8 hours ago
$begingroup$
"unknown" sounds obsolete and unclear. The line equation in the plane $y=x$, here $x,y$ are variables, but the line equation $x=1$, is here $x$ a variable or an unknown? Personally, I use "variable" in all cases.
$endgroup$
– A.Γ.
7 hours ago
add a comment |
2
$begingroup$
It depends on the context. I would call $x$ a variable in both cases and eventually "unknown" if it is apparant that we aim to know which values it can take. Btw, there is also a distinction between free and bound variables. In the expression $int_0^x f(u)du$ variable $x$ is free and variable $u$ is bound.
$endgroup$
– drhab
8 hours ago
$begingroup$
"unknown" sounds obsolete and unclear. The line equation in the plane $y=x$, here $x,y$ are variables, but the line equation $x=1$, is here $x$ a variable or an unknown? Personally, I use "variable" in all cases.
$endgroup$
– A.Γ.
7 hours ago
2
2
$begingroup$
It depends on the context. I would call $x$ a variable in both cases and eventually "unknown" if it is apparant that we aim to know which values it can take. Btw, there is also a distinction between free and bound variables. In the expression $int_0^x f(u)du$ variable $x$ is free and variable $u$ is bound.
$endgroup$
– drhab
8 hours ago
$begingroup$
It depends on the context. I would call $x$ a variable in both cases and eventually "unknown" if it is apparant that we aim to know which values it can take. Btw, there is also a distinction between free and bound variables. In the expression $int_0^x f(u)du$ variable $x$ is free and variable $u$ is bound.
$endgroup$
– drhab
8 hours ago
$begingroup$
"unknown" sounds obsolete and unclear. The line equation in the plane $y=x$, here $x,y$ are variables, but the line equation $x=1$, is here $x$ a variable or an unknown? Personally, I use "variable" in all cases.
$endgroup$
– A.Γ.
7 hours ago
$begingroup$
"unknown" sounds obsolete and unclear. The line equation in the plane $y=x$, here $x,y$ are variables, but the line equation $x=1$, is here $x$ a variable or an unknown? Personally, I use "variable" in all cases.
$endgroup$
– A.Γ.
7 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$x$, if such a notation may be introduced, is always a variable, but there are two different questions:
(1) while $x$ varies, how is another value changing?
(2) while $x$ varies, when (at which value of $x$) does something specific event happen? (A specific event: For example two values get equal.)
answered 8 hours ago
zolizoli
17.3k41945
$endgroup$
add a comment |
$begingroup$
People are free to use the word "variable" for unknowns too, but if we wish to distinguish the terms we can say unknowns are to be obtained, whereas variables are to be discussed generally. For example, $x$ is an unknown in $x+1=2$ but a variable in $(x^2)^prime=2x$, or a law of physics such as $F=fracddtleft(mfracdxdtright)$. But what about $x-3+4=x+1$? Well, $x$ would be an unknown in that if you were thereby trying to solve $x-3+4=2$ by reducing it to the problem above.
answered 8 hours ago
J.G.J.G.
39.2k23758
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
$x$, if such a notation may be introduced, is always a variable, but there are two different questions:
(1) while $x$ varies, how is another value changing?
(2) while $x$ varies, when (at which value of $x$) does something specific event happen? (A specific event: For example two values get equal.)
answered 8 hours ago
zolizoli
17.3k41945
$endgroup$
add a comment |
$begingroup$
$x$, if such a notation may be introduced, is always a variable, but there are two different questions:
(1) while $x$ varies, how is another value changing?
(2) while $x$ varies, when (at which value of $x$) does something specific event happen? (A specific event: For example two values get equal.)
answered 8 hours ago
zolizoli
17.3k41945
$endgroup$
add a comment |
$begingroup$
$x$, if such a notation may be introduced, is always a variable, but there are two different questions:
(1) while $x$ varies, how is another value changing?
(2) while $x$ varies, when (at which value of $x$) does something specific event happen? (A specific event: For example two values get equal.)
answered 8 hours ago
zolizoli
17.3k41945
$endgroup$
$x$, if such a notation may be introduced, is always a variable, but there are two different questions:
(1) while $x$ varies, how is another value changing?
(2) while $x$ varies, when (at which value of $x$) does something specific event happen? (A specific event: For example two values get equal.)
answered 8 hours ago
zolizoli
17.3k41945
answered 8 hours ago
zolizoli
17.3k41945
answered 8 hours ago
zolizoli
17.3k41945
answered 8 hours ago
zolizoli
17.3k41945
17.3k41945
add a comment |
add a comment |
$begingroup$
People are free to use the word "variable" for unknowns too, but if we wish to distinguish the terms we can say unknowns are to be obtained, whereas variables are to be discussed generally. For example, $x$ is an unknown in $x+1=2$ but a variable in $(x^2)^prime=2x$, or a law of physics such as $F=fracddtleft(mfracdxdtright)$. But what about $x-3+4=x+1$? Well, $x$ would be an unknown in that if you were thereby trying to solve $x-3+4=2$ by reducing it to the problem above.
answered 8 hours ago
J.G.J.G.
39.2k23758
$endgroup$
add a comment |
$begingroup$
People are free to use the word "variable" for unknowns too, but if we wish to distinguish the terms we can say unknowns are to be obtained, whereas variables are to be discussed generally. For example, $x$ is an unknown in $x+1=2$ but a variable in $(x^2)^prime=2x$, or a law of physics such as $F=fracddtleft(mfracdxdtright)$. But what about $x-3+4=x+1$? Well, $x$ would be an unknown in that if you were thereby trying to solve $x-3+4=2$ by reducing it to the problem above.
answered 8 hours ago
J.G.J.G.
39.2k23758
$endgroup$
add a comment |
$begingroup$
People are free to use the word "variable" for unknowns too, but if we wish to distinguish the terms we can say unknowns are to be obtained, whereas variables are to be discussed generally. For example, $x$ is an unknown in $x+1=2$ but a variable in $(x^2)^prime=2x$, or a law of physics such as $F=fracddtleft(mfracdxdtright)$. But what about $x-3+4=x+1$? Well, $x$ would be an unknown in that if you were thereby trying to solve $x-3+4=2$ by reducing it to the problem above.
answered 8 hours ago
J.G.J.G.
39.2k23758
$endgroup$
People are free to use the word "variable" for unknowns too, but if we wish to distinguish the terms we can say unknowns are to be obtained, whereas variables are to be discussed generally. For example, $x$ is an unknown in $x+1=2$ but a variable in $(x^2)^prime=2x$, or a law of physics such as $F=fracddtleft(mfracdxdtright)$. But what about $x-3+4=x+1$? Well, $x$ would be an unknown in that if you were thereby trying to solve $x-3+4=2$ by reducing it to the problem above.
answered 8 hours ago
J.G.J.G.
39.2k23758
answered 8 hours ago
J.G.J.G.
39.2k23758
answered 8 hours ago
J.G.J.G.
39.2k23758
answered 8 hours ago
J.G.J.G.
39.2k23758
39.2k23758
add a comment |
add a comment |
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$begingroup$
It depends on the context. I would call $x$ a variable in both cases and eventually "unknown" if it is apparant that we aim to know which values it can take. Btw, there is also a distinction between free and bound variables. In the expression $int_0^x f(u)du$ variable $x$ is free and variable $u$ is bound.
$endgroup$
– drhab
8 hours ago
$begingroup$
"unknown" sounds obsolete and unclear. The line equation in the plane $y=x$, here $x,y$ are variables, but the line equation $x=1$, is here $x$ a variable or an unknown? Personally, I use "variable" in all cases.
$endgroup$
– A.Γ.
7 hours ago