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?
$begingroup$
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
asked Apr 4 at 7:45
cinicocinico
1234
$endgroup$
add a comment |
$begingroup$
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
asked Apr 4 at 7:45
cinicocinico
1234
$endgroup$
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 withtext. 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
add a comment |
$begingroup$
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
asked Apr 4 at 7:45
cinicocinico
1234
$endgroup$
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
asked Apr 4 at 7:45
cinicocinico
1234
asked Apr 4 at 7:45
cinicocinico
1234
edited Apr 4 at 17:32
cinico
asked Apr 4 at 7:45
cinicocinico
1234
asked Apr 4 at 7:45
cinicocinico
1234
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 withtext. 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
add a comment |
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 withtext. 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 $endgroup$
– 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 $endgroup$
– 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
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Open any book in the notation section:
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
$endgroup$
add a comment |
$begingroup$
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 $gapprox9.8$.
edited Apr 5 at 7:21
Community♦
1
answered Apr 4 at 7:55
JosuéJosué
3,51742672
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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?
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Open any book in the notation section:
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
$endgroup$
add a comment |
$begingroup$
Open any book in the notation section:
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
$endgroup$
add a comment |
$begingroup$
Open any book in the notation section:
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
$endgroup$
Open any book in the notation section:
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
answered Apr 4 at 9:33
Yves DaoustYves Daoust
133k676232
133k676232
add a comment |
add a comment |
$begingroup$
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 $gapprox9.8$.
edited Apr 5 at 7:21
Community♦
1
answered Apr 4 at 7:55
JosuéJosué
3,51742672
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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 $gapprox9.8$.
edited Apr 5 at 7:21
Community♦
1
answered Apr 4 at 7:55
JosuéJosué
3,51742672
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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 $gapprox9.8$.
edited Apr 5 at 7:21
Community♦
1
answered Apr 4 at 7:55
JosuéJosué
3,51742672
$endgroup$
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 $gapprox9.8$.
edited Apr 5 at 7:21
Community♦
1
answered Apr 4 at 7:55
JosuéJosué
3,51742672
edited Apr 5 at 7:21
Community♦
1
edited Apr 5 at 7:21
Community♦
1
edited Apr 5 at 7:21
Community♦
1
1
answered Apr 4 at 7:55
JosuéJosué
3,51742672
answered Apr 4 at 7:55
JosuéJosué
3,51742672
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
add a comment |
$begingroup$
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 $gapprox 9.8 mathrmm/texts^2$..."
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– Toffomat
Apr 4 at 8:43
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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 :)
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– 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 :)
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– cinico
Apr 4 at 9:26
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@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.
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– 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.
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– 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.
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– 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
add a comment |
$begingroup$
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?
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
$endgroup$
add a comment |
$begingroup$
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?
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
$endgroup$
add a comment |
$begingroup$
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?
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
$endgroup$
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?
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
edited Apr 4 at 14:31
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
answered Apr 4 at 14:16
James ArathoonJames Arathoon
1,623423
1,623423
add a comment |
add a comment |
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1
$begingroup$
"this is most likely not correct": can you elaborate ? By the way, there is nothing formal here, just natural language.
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– 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.
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– 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
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@leftaroundabout Thanks for teaching me! :)
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– cinico
Apr 4 at 12:57
$begingroup$
Thanks @ToddWilcox. It was a copy/paste thing. Fixed.
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– cinico
Apr 4 at 17:33