What are expressions in mathematics?
$begingroup$
Like algebraic expressions are logarithmic, Experimental, trigonometric, differential, etc., expressions also there?
I am not referring to functions, but just expressions or equations. Are their definitions similar to how we define their corresponding function?
I know Functions are more frequently and widely used than any expression, why?
definition formal-languages
edited Dec 28 '18 at 9:09
Shaun
9,544113684
$endgroup$
add a comment |
$begingroup$
Like algebraic expressions are logarithmic, Experimental, trigonometric, differential, etc., expressions also there?
I am not referring to functions, but just expressions or equations. Are their definitions similar to how we define their corresponding function?
I know Functions are more frequently and widely used than any expression, why?
definition formal-languages
edited Dec 28 '18 at 9:09
Shaun
9,544113684
$endgroup$
$begingroup$
en.wikipedia.org/wiki/Expression_(mathematics)
$endgroup$
– Matti P.
Dec 28 '18 at 8:29
$begingroup$
In my mind, the word "expression" does not have a precise meaning, and if I'm developing math rigorously I would avoid using the word "expression" entirely. (Maybe in some other areas of math like logic the word "expression" is given a precise meaning.)
$endgroup$
– littleO
Dec 28 '18 at 9:32
add a comment |
$begingroup$
Like algebraic expressions are logarithmic, Experimental, trigonometric, differential, etc., expressions also there?
I am not referring to functions, but just expressions or equations. Are their definitions similar to how we define their corresponding function?
I know Functions are more frequently and widely used than any expression, why?
definition formal-languages
edited Dec 28 '18 at 9:09
Shaun
9,544113684
$endgroup$
Like algebraic expressions are logarithmic, Experimental, trigonometric, differential, etc., expressions also there?
I am not referring to functions, but just expressions or equations. Are their definitions similar to how we define their corresponding function?
I know Functions are more frequently and widely used than any expression, why?
definition formal-languages
definition formal-languages
edited Dec 28 '18 at 9:09
Shaun
9,544113684
edited Dec 28 '18 at 9:09
Shaun
9,544113684
edited Dec 28 '18 at 9:09
Shaun
9,544113684
edited Dec 28 '18 at 9:09
Shaun
9,544113684
edited Dec 28 '18 at 9:09
Shaun
9,544113684
9,544113684
asked Dec 28 '18 at 8:26
user629353
$begingroup$
en.wikipedia.org/wiki/Expression_(mathematics)
$endgroup$
– Matti P.
Dec 28 '18 at 8:29
$begingroup$
In my mind, the word "expression" does not have a precise meaning, and if I'm developing math rigorously I would avoid using the word "expression" entirely. (Maybe in some other areas of math like logic the word "expression" is given a precise meaning.)
$endgroup$
– littleO
Dec 28 '18 at 9:32
add a comment |
$begingroup$
en.wikipedia.org/wiki/Expression_(mathematics)
$endgroup$
– Matti P.
Dec 28 '18 at 8:29
$begingroup$
In my mind, the word "expression" does not have a precise meaning, and if I'm developing math rigorously I would avoid using the word "expression" entirely. (Maybe in some other areas of math like logic the word "expression" is given a precise meaning.)
$endgroup$
– littleO
Dec 28 '18 at 9:32
$begingroup$
en.wikipedia.org/wiki/Expression_(mathematics)
$endgroup$
– Matti P.
Dec 28 '18 at 8:29
$begingroup$
en.wikipedia.org/wiki/Expression_(mathematics)
$endgroup$
– Matti P.
Dec 28 '18 at 8:29
$begingroup$
In my mind, the word "expression" does not have a precise meaning, and if I'm developing math rigorously I would avoid using the word "expression" entirely. (Maybe in some other areas of math like logic the word "expression" is given a precise meaning.)
$endgroup$
– littleO
Dec 28 '18 at 9:32
$begingroup$
In my mind, the word "expression" does not have a precise meaning, and if I'm developing math rigorously I would avoid using the word "expression" entirely. (Maybe in some other areas of math like logic the word "expression" is given a precise meaning.)
$endgroup$
– littleO
Dec 28 '18 at 9:32
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
An expression is essentially a string of symbols (e.g., $$frac{-bpmsqrt{b^2-4ac}}{2a}$$ or $x^2$) with some technical requirements; an equation is a relationship between expressions that is given by an equality (e.g., $c=2pi r$).
I doubt that functions are more frequently/widely used than expressions. In mathematical literature, a typical author talks about the LHS or the RHS of the definition of a function (and the derivations thereof) far more often than the function itself. For every equation, there is at least two expressions.
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
$endgroup$
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
1
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
1
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
|
show 2 more comments
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1 Answer
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$begingroup$
An expression is essentially a string of symbols (e.g., $$frac{-bpmsqrt{b^2-4ac}}{2a}$$ or $x^2$) with some technical requirements; an equation is a relationship between expressions that is given by an equality (e.g., $c=2pi r$).
I doubt that functions are more frequently/widely used than expressions. In mathematical literature, a typical author talks about the LHS or the RHS of the definition of a function (and the derivations thereof) far more often than the function itself. For every equation, there is at least two expressions.
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
$endgroup$
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
1
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
1
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
|
show 2 more comments
$begingroup$
An expression is essentially a string of symbols (e.g., $$frac{-bpmsqrt{b^2-4ac}}{2a}$$ or $x^2$) with some technical requirements; an equation is a relationship between expressions that is given by an equality (e.g., $c=2pi r$).
I doubt that functions are more frequently/widely used than expressions. In mathematical literature, a typical author talks about the LHS or the RHS of the definition of a function (and the derivations thereof) far more often than the function itself. For every equation, there is at least two expressions.
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
$endgroup$
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
1
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
1
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
|
show 2 more comments
$begingroup$
An expression is essentially a string of symbols (e.g., $$frac{-bpmsqrt{b^2-4ac}}{2a}$$ or $x^2$) with some technical requirements; an equation is a relationship between expressions that is given by an equality (e.g., $c=2pi r$).
I doubt that functions are more frequently/widely used than expressions. In mathematical literature, a typical author talks about the LHS or the RHS of the definition of a function (and the derivations thereof) far more often than the function itself. For every equation, there is at least two expressions.
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
$endgroup$
An expression is essentially a string of symbols (e.g., $$frac{-bpmsqrt{b^2-4ac}}{2a}$$ or $x^2$) with some technical requirements; an equation is a relationship between expressions that is given by an equality (e.g., $c=2pi r$).
I doubt that functions are more frequently/widely used than expressions. In mathematical literature, a typical author talks about the LHS or the RHS of the definition of a function (and the derivations thereof) far more often than the function itself. For every equation, there is at least two expressions.
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
edited Dec 28 '18 at 9:24
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
answered Dec 28 '18 at 8:30
ShaunShaun
9,544113684
9,544113684
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
1
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
1
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
|
show 2 more comments
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
1
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
1
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
$begingroup$
Aren't Expressions classified on bases of their corresponding functions, like logarithmic expression, trigonometric expression, etc
$endgroup$
– user629353
Dec 28 '18 at 8:33
1
1
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Not necessarily.
$endgroup$
– Shaun
Dec 28 '18 at 8:33
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Then what logx called without equating it to y, and sinx, tanx ,logx should all be then same category expression inspite their corresponding function are different
$endgroup$
– user629353
Dec 28 '18 at 8:35
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
$begingroup$
Well, yeah; you're right. In those cases they are expressions involving those functions.
$endgroup$
– Shaun
Dec 28 '18 at 8:37
1
1
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
$begingroup$
More than just "a string of symbols", an expression has to be a syntactically correct well-formed formula (in some formal language that's usually typical math notation).
$endgroup$
– John Forkosh
Dec 28 '18 at 9:04
|
show 2 more comments
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$begingroup$
en.wikipedia.org/wiki/Expression_(mathematics)
$endgroup$
– Matti P.
Dec 28 '18 at 8:29
$begingroup$
In my mind, the word "expression" does not have a precise meaning, and if I'm developing math rigorously I would avoid using the word "expression" entirely. (Maybe in some other areas of math like logic the word "expression" is given a precise meaning.)
$endgroup$
– littleO
Dec 28 '18 at 9:32