What are expressions in mathematics?












1












$begingroup$


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







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$endgroup$












  • $begingroup$
    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


















1












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    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
















1












1








1





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 28 '18 at 9:09









Shaun

10.5k113687




10.5k113687










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




















  • $begingroup$
    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












1 Answer
1






active

oldest

votes


















1












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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












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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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
















1












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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














1












1








1





$begingroup$

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.






share|cite|improve this answer











$endgroup$



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.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 28 '18 at 9:24

























answered Dec 28 '18 at 8:30









ShaunShaun

10.5k113687




10.5k113687












  • $begingroup$
    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








  • 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


















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