What is the formal way to express the meaning of a variable? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)what is the meaning of the notation $ C^q_c(0,1)$What is the meaning of $mathbb R^+$?What is the meaning of the symbol $pitchfork$?What is the meaning of “$<infty$”?What is the meaning of the notation $]a,b[$?What is the meaning of the notation $]1, 1[$?What is the meaning of $mathbbN_0$?What is the meaning of the math symbol $because$?What is the meaning of the $vdash$ symbol?⊕: What is the meaning of the $oplus$-symbol?

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What is the formal way to express the meaning of a variable?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)what is the meaning of the notation $ C^q_c(0,1)$What is the meaning of $mathbb R^+$?What is the meaning of the symbol $pitchfork$?What is the meaning of “$<infty$”?What is the meaning of the notation $]a,b[$?What is the meaning of the notation $]1, 1[$?What is the meaning of $mathbbN_0$?What is the meaning of the math symbol $because$?What is the meaning of the $vdash$ symbol?⊕: What is the meaning of the $oplus$-symbol?










3












$begingroup$


I would like to know what is the formal way (if any) of defining the meaning of variables. When I start writing a proof, or if I simply want to establish a formal definition, I usually follow the notation below, but I recently understood that this is most likely not correct:



$F_g equivtext''Magnitude of the gravitational force applied to a body, measured in Newtons"$



$g equiv text''Average acceleration at Earth's surface, in meters per squared seconds, caused by gravity''$



$m equivtext''Mass of the body, measured in kilograms''$



$F_g = g times mspace,spacespace g=9.8$



How should I express this information in a formal way?






notation







share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    "this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
    $endgroup$
    – Yves Daoust
    Apr 4 at 8:03











  • $begingroup$
    @YvesDaoust I assumed until recently that the symbol $equiv$ meant "is defined as", when actually the notation ":=" is more correct. Furthermore, as you said, the fact that I'm mixing mathematical notation with natural language doesn't seem very consistent to me. I think I accept the answer that says that, for this type of intent, the best way is to use exclusivelly natural language, not mathematical notation.
    $endgroup$
    – cinico
    Apr 4 at 9:23






  • 1




    $begingroup$
    Whenever you do write chunks of text in a LaTeX formular (which you shouldn't do in this case, but sometimes it can be appropriate), make sure you surround it with text . See $m equiv textForce$ vs $m equiv Force$ (yuk). Also, quoting in LaTeX should be written ``Force'' (two backticks on the left, two single apostrophes on the right) to properly appear as “Force” in the rendered document.
    $endgroup$
    – leftaroundabout
    Apr 4 at 12:00











  • $begingroup$
    @leftaroundabout Thanks for teaching me! :)
    $endgroup$
    – cinico
    Apr 4 at 12:57










  • $begingroup$
    Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
    $endgroup$
    – cinico
    Apr 4 at 17:33















3












$begingroup$


I would like to know what is the formal way (if any) of defining the meaning of variables. When I start writing a proof, or if I simply want to establish a formal definition, I usually follow the notation below, but I recently understood that this is most likely not correct:



$F_g equivtext''Magnitude of the gravitational force applied to a body, measured in Newtons"$



$g equiv text''Average acceleration at Earth's surface, in meters per squared seconds, caused by gravity''$



$m equivtext''Mass of the body, measured in kilograms''$



$F_g = g times mspace,spacespace g=9.8$



How should I express this information in a formal way?






notation







share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    "this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
    $endgroup$
    – Yves Daoust
    Apr 4 at 8:03











  • $begingroup$
    @YvesDaoust I assumed until recently that the symbol $equiv$ meant "is defined as", when actually the notation ":=" is more correct. Furthermore, as you said, the fact that I'm mixing mathematical notation with natural language doesn't seem very consistent to me. I think I accept the answer that says that, for this type of intent, the best way is to use exclusivelly natural language, not mathematical notation.
    $endgroup$
    – cinico
    Apr 4 at 9:23






  • 1




    $begingroup$
    Whenever you do write chunks of text in a LaTeX formular (which you shouldn't do in this case, but sometimes it can be appropriate), make sure you surround it with text . See $m equiv textForce$ vs $m equiv Force$ (yuk). Also, quoting in LaTeX should be written ``Force'' (two backticks on the left, two single apostrophes on the right) to properly appear as “Force” in the rendered document.
    $endgroup$
    – leftaroundabout
    Apr 4 at 12:00











  • $begingroup$
    @leftaroundabout Thanks for teaching me! :)
    $endgroup$
    – cinico
    Apr 4 at 12:57










  • $begingroup$
    Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
    $endgroup$
    – cinico
    Apr 4 at 17:33













3












3








3


1



$begingroup$


I would like to know what is the formal way (if any) of defining the meaning of variables. When I start writing a proof, or if I simply want to establish a formal definition, I usually follow the notation below, but I recently understood that this is most likely not correct:



$F_g equivtext''Magnitude of the gravitational force applied to a body, measured in Newtons"$



$g equiv text''Average acceleration at Earth's surface, in meters per squared seconds, caused by gravity''$



$m equivtext''Mass of the body, measured in kilograms''$



$F_g = g times mspace,spacespace g=9.8$



How should I express this information in a formal way?






notation







share|cite|improve this question











$endgroup$




I would like to know what is the formal way (if any) of defining the meaning of variables. When I start writing a proof, or if I simply want to establish a formal definition, I usually follow the notation below, but I recently understood that this is most likely not correct:



$F_g equivtext''Magnitude of the gravitational force applied to a body, measured in Newtons"$



$g equiv text''Average acceleration at Earth's surface, in meters per squared seconds, caused by gravity''$



$m equivtext''Mass of the body, measured in kilograms''$



$F_g = g times mspace,spacespace g=9.8$



How should I express this information in a formal way?






notation




notation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Apr 4 at 17:32







cinico

















asked Apr 4 at 7:45









cinicocinico

1234




1234







  • 1




    $begingroup$
    "this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
    $endgroup$
    – Yves Daoust
    Apr 4 at 8:03











  • $begingroup$
    @YvesDaoust I assumed until recently that the symbol $equiv$ meant "is defined as", when actually the notation ":=" is more correct. Furthermore, as you said, the fact that I'm mixing mathematical notation with natural language doesn't seem very consistent to me. I think I accept the answer that says that, for this type of intent, the best way is to use exclusivelly natural language, not mathematical notation.
    $endgroup$
    – cinico
    Apr 4 at 9:23






  • 1




    $begingroup$
    Whenever you do write chunks of text in a LaTeX formular (which you shouldn't do in this case, but sometimes it can be appropriate), make sure you surround it with text . See $m equiv textForce$ vs $m equiv Force$ (yuk). Also, quoting in LaTeX should be written ``Force'' (two backticks on the left, two single apostrophes on the right) to properly appear as “Force” in the rendered document.
    $endgroup$
    – leftaroundabout
    Apr 4 at 12:00











  • $begingroup$
    @leftaroundabout Thanks for teaching me! :)
    $endgroup$
    – cinico
    Apr 4 at 12:57










  • $begingroup$
    Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
    $endgroup$
    – cinico
    Apr 4 at 17:33












  • 1




    $begingroup$
    "this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
    $endgroup$
    – Yves Daoust
    Apr 4 at 8:03











  • $begingroup$
    @YvesDaoust I assumed until recently that the symbol $equiv$ meant "is defined as", when actually the notation ":=" is more correct. Furthermore, as you said, the fact that I'm mixing mathematical notation with natural language doesn't seem very consistent to me. I think I accept the answer that says that, for this type of intent, the best way is to use exclusivelly natural language, not mathematical notation.
    $endgroup$
    – cinico
    Apr 4 at 9:23






  • 1




    $begingroup$
    Whenever you do write chunks of text in a LaTeX formular (which you shouldn't do in this case, but sometimes it can be appropriate), make sure you surround it with text . See $m equiv textForce$ vs $m equiv Force$ (yuk). Also, quoting in LaTeX should be written ``Force'' (two backticks on the left, two single apostrophes on the right) to properly appear as “Force” in the rendered document.
    $endgroup$
    – leftaroundabout
    Apr 4 at 12:00











  • $begingroup$
    @leftaroundabout Thanks for teaching me! :)
    $endgroup$
    – cinico
    Apr 4 at 12:57










  • $begingroup$
    Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
    $endgroup$
    – cinico
    Apr 4 at 17:33







1




1




$begingroup$
"this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
$endgroup$
– Yves Daoust
Apr 4 at 8:03





$begingroup$
"this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
$endgroup$
– Yves Daoust
Apr 4 at 8:03













$begingroup$
@YvesDaoust I assumed until recently that the symbol $equiv$ meant "is defined as", when actually the notation ":=" is more correct. Furthermore, as you said, the fact that I'm mixing mathematical notation with natural language doesn't seem very consistent to me. I think I accept the answer that says that, for this type of intent, the best way is to use exclusivelly natural language, not mathematical notation.
$endgroup$
– cinico
Apr 4 at 9:23




$begingroup$
@YvesDaoust I assumed until recently that the symbol $equiv$ meant "is defined as", when actually the notation ":=" is more correct. Furthermore, as you said, the fact that I'm mixing mathematical notation with natural language doesn't seem very consistent to me. I think I accept the answer that says that, for this type of intent, the best way is to use exclusivelly natural language, not mathematical notation.
$endgroup$
– cinico
Apr 4 at 9:23




1




1




$begingroup$
Whenever you do write chunks of text in a LaTeX formular (which you shouldn't do in this case, but sometimes it can be appropriate), make sure you surround it with text . See $m equiv textForce$ vs $m equiv Force$ (yuk). Also, quoting in LaTeX should be written ``Force'' (two backticks on the left, two single apostrophes on the right) to properly appear as “Force” in the rendered document.
$endgroup$
– leftaroundabout
Apr 4 at 12:00





$begingroup$
Whenever you do write chunks of text in a LaTeX formular (which you shouldn't do in this case, but sometimes it can be appropriate), make sure you surround it with text . See $m equiv textForce$ vs $m equiv Force$ (yuk). Also, quoting in LaTeX should be written ``Force'' (two backticks on the left, two single apostrophes on the right) to properly appear as “Force” in the rendered document.
$endgroup$
– leftaroundabout
Apr 4 at 12:00













$begingroup$
@leftaroundabout Thanks for teaching me! :)
$endgroup$
– cinico
Apr 4 at 12:57




$begingroup$
@leftaroundabout Thanks for teaching me! :)
$endgroup$
– cinico
Apr 4 at 12:57












$begingroup$
Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
$endgroup$
– cinico
Apr 4 at 17:33




$begingroup$
Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
$endgroup$
– cinico
Apr 4 at 17:33










3 Answers
3






active

oldest

votes


















8












$begingroup$

Open any book in the notation section:



enter image description here



enter image description here



enter image description here






share|cite|improve this answer









$endgroup$




















    9












    $begingroup$

    I live by the mantra that math should be written as though it is natural language, punctuation included. So, in your shoes, I would write:




    Let $F_g$ be the magnitude of the gravitational force applied to a body, measured in Newtons; let $g$ be the average acceleration at Earth's surface, caused by gravity, measured in meters per squared seconds; and let $m$ be the mass of this body, measured in kilograms. Then $F_g=gm$, where $gapprox9.8$.







    share|cite|improve this answer











    $endgroup$












    • $begingroup$
      Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
      $endgroup$
      – 5xum
      Apr 4 at 8:01






    • 8




      $begingroup$
      Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
      $endgroup$
      – Toffomat
      Apr 4 at 8:43











    • $begingroup$
      Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
      $endgroup$
      – cinico
      Apr 4 at 9:26










    • $begingroup$
      @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
      $endgroup$
      – user21820
      Apr 4 at 12:07










    • $begingroup$
      In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
      $endgroup$
      – Todd Wilcox
      Apr 4 at 15:15



















    0












    $begingroup$

    One can always nit pick about "formality", or indeed "verifiability", if you want to revive the failed philosophical project, called logical positivism, from the first half of the twentieth century. For example:



    "average acceleration at [the] Earth's surface, caused by gravity"



    This statement, in mathematical, physical and engineering terms, is quite a claim if you really think about it.



    The acceleration measured at the earths surface varies with height above sea level, potentially has other measurable components other than the main (unspecified) vertical one, especially so if you live next to a mountain, and has a component due to the rotation of the earth which varies with latitude.



    The question is:



    What set of measurements is the acceleration you refer to the (mathematical) average of?






    share|cite|improve this answer











    $endgroup$













      Your Answer








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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      8












      $begingroup$

      Open any book in the notation section:



      enter image description here



      enter image description here



      enter image description here






      share|cite|improve this answer









      $endgroup$

















        8












        $begingroup$

        Open any book in the notation section:



        enter image description here



        enter image description here



        enter image description here






        share|cite|improve this answer









        $endgroup$















          8












          8








          8





          $begingroup$

          Open any book in the notation section:



          enter image description here



          enter image description here



          enter image description here






          share|cite|improve this answer









          $endgroup$



          Open any book in the notation section:



          enter image description here



          enter image description here



          enter image description here







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Apr 4 at 9:33









          Yves DaoustYves Daoust

          133k676232




          133k676232





















              9












              $begingroup$

              I live by the mantra that math should be written as though it is natural language, punctuation included. So, in your shoes, I would write:




              Let $F_g$ be the magnitude of the gravitational force applied to a body, measured in Newtons; let $g$ be the average acceleration at Earth's surface, caused by gravity, measured in meters per squared seconds; and let $m$ be the mass of this body, measured in kilograms. Then $F_g=gm$, where $gapprox9.8$.







              share|cite|improve this answer











              $endgroup$












              • $begingroup$
                Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
                $endgroup$
                – 5xum
                Apr 4 at 8:01






              • 8




                $begingroup$
                Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
                $endgroup$
                – Toffomat
                Apr 4 at 8:43











              • $begingroup$
                Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
                $endgroup$
                – cinico
                Apr 4 at 9:26










              • $begingroup$
                @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
                $endgroup$
                – user21820
                Apr 4 at 12:07










              • $begingroup$
                In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
                $endgroup$
                – Todd Wilcox
                Apr 4 at 15:15
















              9












              $begingroup$

              I live by the mantra that math should be written as though it is natural language, punctuation included. So, in your shoes, I would write:




              Let $F_g$ be the magnitude of the gravitational force applied to a body, measured in Newtons; let $g$ be the average acceleration at Earth's surface, caused by gravity, measured in meters per squared seconds; and let $m$ be the mass of this body, measured in kilograms. Then $F_g=gm$, where $gapprox9.8$.







              share|cite|improve this answer











              $endgroup$












              • $begingroup$
                Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
                $endgroup$
                – 5xum
                Apr 4 at 8:01






              • 8




                $begingroup$
                Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
                $endgroup$
                – Toffomat
                Apr 4 at 8:43











              • $begingroup$
                Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
                $endgroup$
                – cinico
                Apr 4 at 9:26










              • $begingroup$
                @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
                $endgroup$
                – user21820
                Apr 4 at 12:07










              • $begingroup$
                In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
                $endgroup$
                – Todd Wilcox
                Apr 4 at 15:15














              9












              9








              9





              $begingroup$

              I live by the mantra that math should be written as though it is natural language, punctuation included. So, in your shoes, I would write:




              Let $F_g$ be the magnitude of the gravitational force applied to a body, measured in Newtons; let $g$ be the average acceleration at Earth's surface, caused by gravity, measured in meters per squared seconds; and let $m$ be the mass of this body, measured in kilograms. Then $F_g=gm$, where $gapprox9.8$.







              share|cite|improve this answer











              $endgroup$



              I live by the mantra that math should be written as though it is natural language, punctuation included. So, in your shoes, I would write:




              Let $F_g$ be the magnitude of the gravitational force applied to a body, measured in Newtons; let $g$ be the average acceleration at Earth's surface, caused by gravity, measured in meters per squared seconds; and let $m$ be the mass of this body, measured in kilograms. Then $F_g=gm$, where $gapprox9.8$.








              share|cite|improve this answer














              share|cite|improve this answer



              share|cite|improve this answer








              edited Apr 5 at 7:21









              Community♦

              1




              1










              answered Apr 4 at 7:55









              JosuéJosué

              3,51742672




              3,51742672











              • $begingroup$
                Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
                $endgroup$
                – 5xum
                Apr 4 at 8:01






              • 8




                $begingroup$
                Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
                $endgroup$
                – Toffomat
                Apr 4 at 8:43











              • $begingroup$
                Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
                $endgroup$
                – cinico
                Apr 4 at 9:26










              • $begingroup$
                @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
                $endgroup$
                – user21820
                Apr 4 at 12:07










              • $begingroup$
                In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
                $endgroup$
                – Todd Wilcox
                Apr 4 at 15:15

















              • $begingroup$
                Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
                $endgroup$
                – 5xum
                Apr 4 at 8:01






              • 8




                $begingroup$
                Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
                $endgroup$
                – Toffomat
                Apr 4 at 8:43











              • $begingroup$
                Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
                $endgroup$
                – cinico
                Apr 4 at 9:26










              • $begingroup$
                @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
                $endgroup$
                – user21820
                Apr 4 at 12:07










              • $begingroup$
                In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
                $endgroup$
                – Todd Wilcox
                Apr 4 at 15:15
















              $begingroup$
              Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
              $endgroup$
              – 5xum
              Apr 4 at 8:01




              $begingroup$
              Can confirm. Scientific articles always (well, should always) explain the meanings of their variables in plain language.
              $endgroup$
              – 5xum
              Apr 4 at 8:01




              8




              8




              $begingroup$
              Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
              $endgroup$
              – Toffomat
              Apr 4 at 8:43





              $begingroup$
              Agree with the natural-language mantra. However, I'd prefer leaving out the units in the description, after all the equation holds independent of the units: "Left $F$ be the [,..] force, let $g$ be the acceleration [...] then $F=gm$ where $gapprox 9.8 mathrmm/texts^2$..."
              $endgroup$
              – Toffomat
              Apr 4 at 8:43













              $begingroup$
              Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
              $endgroup$
              – cinico
              Apr 4 at 9:26




              $begingroup$
              Thanks. While I am aware of this way of expressing the meaning, somehow I miss a more clean (almost bullet type) way of stating the definitions. I accept that it's best to use exclusivelly natural language for the definition, and nothing forbids me to format the text to more clean way :)
              $endgroup$
              – cinico
              Apr 4 at 9:26












              $begingroup$
              @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
              $endgroup$
              – user21820
              Apr 4 at 12:07




              $begingroup$
              @cinico: There's nothing wrong with putting Cleric's answer into point form, one point for each definition. I don't think it's fair to claim that mathematics can ever be written as though it is natural language. It isn't natural and never will be. However, it is best expressed in semi-natural language, mixing natural language and mathematical symbols in a way that is most suitable for reader consumption.
              $endgroup$
              – user21820
              Apr 4 at 12:07












              $begingroup$
              In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
              $endgroup$
              – Todd Wilcox
              Apr 4 at 15:15





              $begingroup$
              In the quoted section, did you mean to write "and let $m$ be the mass of the body in question, in kilograms"? Not only are kilograms units of mass, not force, but if $m$ represents mass and not force, then the formula stated makes more sense. Oh I just noticed you were quoting the question. Might make sense to fix it anyway to prevent confusion.
              $endgroup$
              – Todd Wilcox
              Apr 4 at 15:15












              0












              $begingroup$

              One can always nit pick about "formality", or indeed "verifiability", if you want to revive the failed philosophical project, called logical positivism, from the first half of the twentieth century. For example:



              "average acceleration at [the] Earth's surface, caused by gravity"



              This statement, in mathematical, physical and engineering terms, is quite a claim if you really think about it.



              The acceleration measured at the earths surface varies with height above sea level, potentially has other measurable components other than the main (unspecified) vertical one, especially so if you live next to a mountain, and has a component due to the rotation of the earth which varies with latitude.



              The question is:



              What set of measurements is the acceleration you refer to the (mathematical) average of?






              share|cite|improve this answer











              $endgroup$

















                0












                $begingroup$

                One can always nit pick about "formality", or indeed "verifiability", if you want to revive the failed philosophical project, called logical positivism, from the first half of the twentieth century. For example:



                "average acceleration at [the] Earth's surface, caused by gravity"



                This statement, in mathematical, physical and engineering terms, is quite a claim if you really think about it.



                The acceleration measured at the earths surface varies with height above sea level, potentially has other measurable components other than the main (unspecified) vertical one, especially so if you live next to a mountain, and has a component due to the rotation of the earth which varies with latitude.



                The question is:



                What set of measurements is the acceleration you refer to the (mathematical) average of?






                share|cite|improve this answer











                $endgroup$















                  0












                  0








                  0





                  $begingroup$

                  One can always nit pick about "formality", or indeed "verifiability", if you want to revive the failed philosophical project, called logical positivism, from the first half of the twentieth century. For example:



                  "average acceleration at [the] Earth's surface, caused by gravity"



                  This statement, in mathematical, physical and engineering terms, is quite a claim if you really think about it.



                  The acceleration measured at the earths surface varies with height above sea level, potentially has other measurable components other than the main (unspecified) vertical one, especially so if you live next to a mountain, and has a component due to the rotation of the earth which varies with latitude.



                  The question is:



                  What set of measurements is the acceleration you refer to the (mathematical) average of?






                  share|cite|improve this answer











                  $endgroup$



                  One can always nit pick about "formality", or indeed "verifiability", if you want to revive the failed philosophical project, called logical positivism, from the first half of the twentieth century. For example:



                  "average acceleration at [the] Earth's surface, caused by gravity"



                  This statement, in mathematical, physical and engineering terms, is quite a claim if you really think about it.



                  The acceleration measured at the earths surface varies with height above sea level, potentially has other measurable components other than the main (unspecified) vertical one, especially so if you live next to a mountain, and has a component due to the rotation of the earth which varies with latitude.



                  The question is:



                  What set of measurements is the acceleration you refer to the (mathematical) average of?







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Apr 4 at 14:31

























                  answered Apr 4 at 14:16









                  James ArathoonJames Arathoon

                  1,623423




                  1,623423



























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