What's the difference between a “mapping” and “function”?












10












$begingroup$


I think that a mapping and function are the same; there's only a difference between a mapping and relation. But I'm confused. What's the difference between a relation and a mapping and a function?










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  • 2




    $begingroup$
    I think you're right. I don't know any difference between mapping and function.
    $endgroup$
    – Yanko
    7 hours ago










  • $begingroup$
    This depends on the text. Sometimes a mapping is a continuous function, sometimes it's any function at all.
    $endgroup$
    – Mark S.
    6 hours ago










  • $begingroup$
    @MarkS.: often, the books that assume that mappings are continuous mention it somewhere near the beginner, but it is easy to miss.
    $endgroup$
    – Taladris
    1 hour ago
















10












$begingroup$


I think that a mapping and function are the same; there's only a difference between a mapping and relation. But I'm confused. What's the difference between a relation and a mapping and a function?










share|cite|improve this question









New contributor




user634631 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 2




    $begingroup$
    I think you're right. I don't know any difference between mapping and function.
    $endgroup$
    – Yanko
    7 hours ago










  • $begingroup$
    This depends on the text. Sometimes a mapping is a continuous function, sometimes it's any function at all.
    $endgroup$
    – Mark S.
    6 hours ago










  • $begingroup$
    @MarkS.: often, the books that assume that mappings are continuous mention it somewhere near the beginner, but it is easy to miss.
    $endgroup$
    – Taladris
    1 hour ago














10












10








10


3



$begingroup$


I think that a mapping and function are the same; there's only a difference between a mapping and relation. But I'm confused. What's the difference between a relation and a mapping and a function?










share|cite|improve this question









New contributor




user634631 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I think that a mapping and function are the same; there's only a difference between a mapping and relation. But I'm confused. What's the difference between a relation and a mapping and a function?







functions terminology definition






share|cite|improve this question









New contributor




user634631 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









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user634631 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 1 min ago









Mike Pierce

11.4k103583




11.4k103583






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asked 7 hours ago









user634631user634631

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533




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user634631 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





user634631 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






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Check out our Code of Conduct.








  • 2




    $begingroup$
    I think you're right. I don't know any difference between mapping and function.
    $endgroup$
    – Yanko
    7 hours ago










  • $begingroup$
    This depends on the text. Sometimes a mapping is a continuous function, sometimes it's any function at all.
    $endgroup$
    – Mark S.
    6 hours ago










  • $begingroup$
    @MarkS.: often, the books that assume that mappings are continuous mention it somewhere near the beginner, but it is easy to miss.
    $endgroup$
    – Taladris
    1 hour ago














  • 2




    $begingroup$
    I think you're right. I don't know any difference between mapping and function.
    $endgroup$
    – Yanko
    7 hours ago










  • $begingroup$
    This depends on the text. Sometimes a mapping is a continuous function, sometimes it's any function at all.
    $endgroup$
    – Mark S.
    6 hours ago










  • $begingroup$
    @MarkS.: often, the books that assume that mappings are continuous mention it somewhere near the beginner, but it is easy to miss.
    $endgroup$
    – Taladris
    1 hour ago








2




2




$begingroup$
I think you're right. I don't know any difference between mapping and function.
$endgroup$
– Yanko
7 hours ago




$begingroup$
I think you're right. I don't know any difference between mapping and function.
$endgroup$
– Yanko
7 hours ago












$begingroup$
This depends on the text. Sometimes a mapping is a continuous function, sometimes it's any function at all.
$endgroup$
– Mark S.
6 hours ago




$begingroup$
This depends on the text. Sometimes a mapping is a continuous function, sometimes it's any function at all.
$endgroup$
– Mark S.
6 hours ago












$begingroup$
@MarkS.: often, the books that assume that mappings are continuous mention it somewhere near the beginner, but it is easy to miss.
$endgroup$
– Taladris
1 hour ago




$begingroup$
@MarkS.: often, the books that assume that mappings are continuous mention it somewhere near the beginner, but it is easy to miss.
$endgroup$
– Taladris
1 hour ago










4 Answers
4






active

oldest

votes


















4












$begingroup$

Good question. I can give you a simple example.




You can generally think of relations as functions in a higher dimensional space, intersected with a zero plane.




So for example, lets take a parabola and a circle to demonstrate this. Imagine the parabola



$$ f(x) = x^2 + 3x $$



This is clearly a function of x, because if you give me an x value, I can give
you the corresponding value of f(x)
- a mapping is really just another name
for a function. If we want to graph it, we can let the y value
equal the output of $f$, so we would get this graph:



enter image description here



On the other hand, if we graph a circle, like:



$$x^2+y^2=4$$



Its graph is given by:



enter image description here



Now this is fundamentally different to the function. If you wanted the y value at x = 0,
I can't point to a unique value, I'd have to say y = 2 or y = -2. A function can only
have one output. So we have to call this a relation.



Higher Dimensions



However, we can use a clever trick for this circle. We can rewrite it as:



$$ x^2 + y^2 - 4 = 0 $$



Which is obviously the same thing, but on the left hand side, notice that we now
have a function of (x,y), so we can think of this like:



$$ g(x, y) = 0 $$



In a higher dimension, this would be the intersection between the shapes:



$$ z = g(x, y) $$



and



$$ z = 0 $$



Which I've shown below:



enter image description here



Notice that same circle hiding in plain sight.



Key takeaway (tl;dr)




Relations are functions in a higher dimension, intersected with a zero plane
in the higher dimension.







share|cite|improve this answer











$endgroup$













  • $begingroup$
    You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
    $endgroup$
    – Caleth
    4 hours ago








  • 1




    $begingroup$
    The circle is hiding in plane sight.
    $endgroup$
    – Minix
    4 hours ago






  • 5




    $begingroup$
    This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
    $endgroup$
    – Tobias Kildetoft
    2 hours ago






  • 1




    $begingroup$
    I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
    $endgroup$
    – Taladris
    1 hour ago












  • $begingroup$
    While the pictures look nice, I don't really think this is an accurate description of "relation".
    $endgroup$
    – BigbearZzz
    36 mins ago



















7












$begingroup$

Mathematically speaking, a mapping and a function are the same. We called the relation
$$
f={(x,y)in Xtimes Y : text{For all $x$ there exists a unique $y$ such that $(x,y)in f$} }
$$

a function from $X$ to $Y$, denoted by $f:Xto Y$. A mapping is just another word for a function, i.e. a relation that pairs exactly one element of $Y$ to each element of $X$.



In practice, sometime one word is preferred over another, depending on the context.



The word mapping is usually used when we want to view $f:Xto Y$ as a transformation of one object to another. For instance, a linear mapping $T:V to W$ signifies that we want to view $T$ as a transformation of $vin V$ to the vector $Tvin W$. Another example is a conformal map, which transforms a domain in $Bbb C$ to another domain.



The word function is used more often and in various contexts. For example, when we want to view $f:Xto Y$ as a graph in $Xtimes Y$.






share|cite|improve this answer











$endgroup$





















    5












    $begingroup$

    There is basically no difference between mapping and function. In algebra, one uses the notion of operation which is the same as mapping or function. The notion of relation is more general. Functions are specific relations (those which are left-total and right-unique).






    share|cite|improve this answer









    $endgroup$





















      0












      $begingroup$

      Relation and Function are quite different as the later only consider unique images.



      There's not much difference between a mapping and function. The only difference that I can think of is that mapping is just the diagramatical representation of a function or an arrow diagram representation of a function which is quite clear for functions defined on the finite sets, while for infinite sets the two notions coincide.



      I Hope it Helps...






      share|cite|improve this answer









      $endgroup$













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        4 Answers
        4






        active

        oldest

        votes








        4 Answers
        4






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        4












        $begingroup$

        Good question. I can give you a simple example.




        You can generally think of relations as functions in a higher dimensional space, intersected with a zero plane.




        So for example, lets take a parabola and a circle to demonstrate this. Imagine the parabola



        $$ f(x) = x^2 + 3x $$



        This is clearly a function of x, because if you give me an x value, I can give
        you the corresponding value of f(x)
        - a mapping is really just another name
        for a function. If we want to graph it, we can let the y value
        equal the output of $f$, so we would get this graph:



        enter image description here



        On the other hand, if we graph a circle, like:



        $$x^2+y^2=4$$



        Its graph is given by:



        enter image description here



        Now this is fundamentally different to the function. If you wanted the y value at x = 0,
        I can't point to a unique value, I'd have to say y = 2 or y = -2. A function can only
        have one output. So we have to call this a relation.



        Higher Dimensions



        However, we can use a clever trick for this circle. We can rewrite it as:



        $$ x^2 + y^2 - 4 = 0 $$



        Which is obviously the same thing, but on the left hand side, notice that we now
        have a function of (x,y), so we can think of this like:



        $$ g(x, y) = 0 $$



        In a higher dimension, this would be the intersection between the shapes:



        $$ z = g(x, y) $$



        and



        $$ z = 0 $$



        Which I've shown below:



        enter image description here



        Notice that same circle hiding in plain sight.



        Key takeaway (tl;dr)




        Relations are functions in a higher dimension, intersected with a zero plane
        in the higher dimension.







        share|cite|improve this answer











        $endgroup$













        • $begingroup$
          You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
          $endgroup$
          – Caleth
          4 hours ago








        • 1




          $begingroup$
          The circle is hiding in plane sight.
          $endgroup$
          – Minix
          4 hours ago






        • 5




          $begingroup$
          This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
          $endgroup$
          – Tobias Kildetoft
          2 hours ago






        • 1




          $begingroup$
          I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
          $endgroup$
          – Taladris
          1 hour ago












        • $begingroup$
          While the pictures look nice, I don't really think this is an accurate description of "relation".
          $endgroup$
          – BigbearZzz
          36 mins ago
















        4












        $begingroup$

        Good question. I can give you a simple example.




        You can generally think of relations as functions in a higher dimensional space, intersected with a zero plane.




        So for example, lets take a parabola and a circle to demonstrate this. Imagine the parabola



        $$ f(x) = x^2 + 3x $$



        This is clearly a function of x, because if you give me an x value, I can give
        you the corresponding value of f(x)
        - a mapping is really just another name
        for a function. If we want to graph it, we can let the y value
        equal the output of $f$, so we would get this graph:



        enter image description here



        On the other hand, if we graph a circle, like:



        $$x^2+y^2=4$$



        Its graph is given by:



        enter image description here



        Now this is fundamentally different to the function. If you wanted the y value at x = 0,
        I can't point to a unique value, I'd have to say y = 2 or y = -2. A function can only
        have one output. So we have to call this a relation.



        Higher Dimensions



        However, we can use a clever trick for this circle. We can rewrite it as:



        $$ x^2 + y^2 - 4 = 0 $$



        Which is obviously the same thing, but on the left hand side, notice that we now
        have a function of (x,y), so we can think of this like:



        $$ g(x, y) = 0 $$



        In a higher dimension, this would be the intersection between the shapes:



        $$ z = g(x, y) $$



        and



        $$ z = 0 $$



        Which I've shown below:



        enter image description here



        Notice that same circle hiding in plain sight.



        Key takeaway (tl;dr)




        Relations are functions in a higher dimension, intersected with a zero plane
        in the higher dimension.







        share|cite|improve this answer











        $endgroup$













        • $begingroup$
          You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
          $endgroup$
          – Caleth
          4 hours ago








        • 1




          $begingroup$
          The circle is hiding in plane sight.
          $endgroup$
          – Minix
          4 hours ago






        • 5




          $begingroup$
          This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
          $endgroup$
          – Tobias Kildetoft
          2 hours ago






        • 1




          $begingroup$
          I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
          $endgroup$
          – Taladris
          1 hour ago












        • $begingroup$
          While the pictures look nice, I don't really think this is an accurate description of "relation".
          $endgroup$
          – BigbearZzz
          36 mins ago














        4












        4








        4





        $begingroup$

        Good question. I can give you a simple example.




        You can generally think of relations as functions in a higher dimensional space, intersected with a zero plane.




        So for example, lets take a parabola and a circle to demonstrate this. Imagine the parabola



        $$ f(x) = x^2 + 3x $$



        This is clearly a function of x, because if you give me an x value, I can give
        you the corresponding value of f(x)
        - a mapping is really just another name
        for a function. If we want to graph it, we can let the y value
        equal the output of $f$, so we would get this graph:



        enter image description here



        On the other hand, if we graph a circle, like:



        $$x^2+y^2=4$$



        Its graph is given by:



        enter image description here



        Now this is fundamentally different to the function. If you wanted the y value at x = 0,
        I can't point to a unique value, I'd have to say y = 2 or y = -2. A function can only
        have one output. So we have to call this a relation.



        Higher Dimensions



        However, we can use a clever trick for this circle. We can rewrite it as:



        $$ x^2 + y^2 - 4 = 0 $$



        Which is obviously the same thing, but on the left hand side, notice that we now
        have a function of (x,y), so we can think of this like:



        $$ g(x, y) = 0 $$



        In a higher dimension, this would be the intersection between the shapes:



        $$ z = g(x, y) $$



        and



        $$ z = 0 $$



        Which I've shown below:



        enter image description here



        Notice that same circle hiding in plain sight.



        Key takeaway (tl;dr)




        Relations are functions in a higher dimension, intersected with a zero plane
        in the higher dimension.







        share|cite|improve this answer











        $endgroup$



        Good question. I can give you a simple example.




        You can generally think of relations as functions in a higher dimensional space, intersected with a zero plane.




        So for example, lets take a parabola and a circle to demonstrate this. Imagine the parabola



        $$ f(x) = x^2 + 3x $$



        This is clearly a function of x, because if you give me an x value, I can give
        you the corresponding value of f(x)
        - a mapping is really just another name
        for a function. If we want to graph it, we can let the y value
        equal the output of $f$, so we would get this graph:



        enter image description here



        On the other hand, if we graph a circle, like:



        $$x^2+y^2=4$$



        Its graph is given by:



        enter image description here



        Now this is fundamentally different to the function. If you wanted the y value at x = 0,
        I can't point to a unique value, I'd have to say y = 2 or y = -2. A function can only
        have one output. So we have to call this a relation.



        Higher Dimensions



        However, we can use a clever trick for this circle. We can rewrite it as:



        $$ x^2 + y^2 - 4 = 0 $$



        Which is obviously the same thing, but on the left hand side, notice that we now
        have a function of (x,y), so we can think of this like:



        $$ g(x, y) = 0 $$



        In a higher dimension, this would be the intersection between the shapes:



        $$ z = g(x, y) $$



        and



        $$ z = 0 $$



        Which I've shown below:



        enter image description here



        Notice that same circle hiding in plain sight.



        Key takeaway (tl;dr)




        Relations are functions in a higher dimension, intersected with a zero plane
        in the higher dimension.








        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited 6 hours ago

























        answered 6 hours ago









        user2662833user2662833

        1,040815




        1,040815












        • $begingroup$
          You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
          $endgroup$
          – Caleth
          4 hours ago








        • 1




          $begingroup$
          The circle is hiding in plane sight.
          $endgroup$
          – Minix
          4 hours ago






        • 5




          $begingroup$
          This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
          $endgroup$
          – Tobias Kildetoft
          2 hours ago






        • 1




          $begingroup$
          I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
          $endgroup$
          – Taladris
          1 hour ago












        • $begingroup$
          While the pictures look nice, I don't really think this is an accurate description of "relation".
          $endgroup$
          – BigbearZzz
          36 mins ago


















        • $begingroup$
          You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
          $endgroup$
          – Caleth
          4 hours ago








        • 1




          $begingroup$
          The circle is hiding in plane sight.
          $endgroup$
          – Minix
          4 hours ago






        • 5




          $begingroup$
          This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
          $endgroup$
          – Tobias Kildetoft
          2 hours ago






        • 1




          $begingroup$
          I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
          $endgroup$
          – Taladris
          1 hour ago












        • $begingroup$
          While the pictures look nice, I don't really think this is an accurate description of "relation".
          $endgroup$
          – BigbearZzz
          36 mins ago
















        $begingroup$
        You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
        $endgroup$
        – Caleth
        4 hours ago






        $begingroup$
        You don't need it to be a zero plane, it's equivalent to intersect $ z = x^2 + y^2 $ with $ z = 4 $
        $endgroup$
        – Caleth
        4 hours ago






        1




        1




        $begingroup$
        The circle is hiding in plane sight.
        $endgroup$
        – Minix
        4 hours ago




        $begingroup$
        The circle is hiding in plane sight.
        $endgroup$
        – Minix
        4 hours ago




        5




        5




        $begingroup$
        This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
        $endgroup$
        – Tobias Kildetoft
        2 hours ago




        $begingroup$
        This is a pretty imprecise way to phrase things. What does "higher dimension" mean in general? What does a zero plane mean in general? Functions and relations are not something constrained to the real numbers and the like.
        $endgroup$
        – Tobias Kildetoft
        2 hours ago




        1




        1




        $begingroup$
        I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
        $endgroup$
        – Taladris
        1 hour ago






        $begingroup$
        I am not sure I am following. How do you describe the usual order relation on R (real numbers) as an intersection? Are you confusing equation and relation?
        $endgroup$
        – Taladris
        1 hour ago














        $begingroup$
        While the pictures look nice, I don't really think this is an accurate description of "relation".
        $endgroup$
        – BigbearZzz
        36 mins ago




        $begingroup$
        While the pictures look nice, I don't really think this is an accurate description of "relation".
        $endgroup$
        – BigbearZzz
        36 mins ago











        7












        $begingroup$

        Mathematically speaking, a mapping and a function are the same. We called the relation
        $$
        f={(x,y)in Xtimes Y : text{For all $x$ there exists a unique $y$ such that $(x,y)in f$} }
        $$

        a function from $X$ to $Y$, denoted by $f:Xto Y$. A mapping is just another word for a function, i.e. a relation that pairs exactly one element of $Y$ to each element of $X$.



        In practice, sometime one word is preferred over another, depending on the context.



        The word mapping is usually used when we want to view $f:Xto Y$ as a transformation of one object to another. For instance, a linear mapping $T:V to W$ signifies that we want to view $T$ as a transformation of $vin V$ to the vector $Tvin W$. Another example is a conformal map, which transforms a domain in $Bbb C$ to another domain.



        The word function is used more often and in various contexts. For example, when we want to view $f:Xto Y$ as a graph in $Xtimes Y$.






        share|cite|improve this answer











        $endgroup$


















          7












          $begingroup$

          Mathematically speaking, a mapping and a function are the same. We called the relation
          $$
          f={(x,y)in Xtimes Y : text{For all $x$ there exists a unique $y$ such that $(x,y)in f$} }
          $$

          a function from $X$ to $Y$, denoted by $f:Xto Y$. A mapping is just another word for a function, i.e. a relation that pairs exactly one element of $Y$ to each element of $X$.



          In practice, sometime one word is preferred over another, depending on the context.



          The word mapping is usually used when we want to view $f:Xto Y$ as a transformation of one object to another. For instance, a linear mapping $T:V to W$ signifies that we want to view $T$ as a transformation of $vin V$ to the vector $Tvin W$. Another example is a conformal map, which transforms a domain in $Bbb C$ to another domain.



          The word function is used more often and in various contexts. For example, when we want to view $f:Xto Y$ as a graph in $Xtimes Y$.






          share|cite|improve this answer











          $endgroup$
















            7












            7








            7





            $begingroup$

            Mathematically speaking, a mapping and a function are the same. We called the relation
            $$
            f={(x,y)in Xtimes Y : text{For all $x$ there exists a unique $y$ such that $(x,y)in f$} }
            $$

            a function from $X$ to $Y$, denoted by $f:Xto Y$. A mapping is just another word for a function, i.e. a relation that pairs exactly one element of $Y$ to each element of $X$.



            In practice, sometime one word is preferred over another, depending on the context.



            The word mapping is usually used when we want to view $f:Xto Y$ as a transformation of one object to another. For instance, a linear mapping $T:V to W$ signifies that we want to view $T$ as a transformation of $vin V$ to the vector $Tvin W$. Another example is a conformal map, which transforms a domain in $Bbb C$ to another domain.



            The word function is used more often and in various contexts. For example, when we want to view $f:Xto Y$ as a graph in $Xtimes Y$.






            share|cite|improve this answer











            $endgroup$



            Mathematically speaking, a mapping and a function are the same. We called the relation
            $$
            f={(x,y)in Xtimes Y : text{For all $x$ there exists a unique $y$ such that $(x,y)in f$} }
            $$

            a function from $X$ to $Y$, denoted by $f:Xto Y$. A mapping is just another word for a function, i.e. a relation that pairs exactly one element of $Y$ to each element of $X$.



            In practice, sometime one word is preferred over another, depending on the context.



            The word mapping is usually used when we want to view $f:Xto Y$ as a transformation of one object to another. For instance, a linear mapping $T:V to W$ signifies that we want to view $T$ as a transformation of $vin V$ to the vector $Tvin W$. Another example is a conformal map, which transforms a domain in $Bbb C$ to another domain.



            The word function is used more often and in various contexts. For example, when we want to view $f:Xto Y$ as a graph in $Xtimes Y$.







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited 35 mins ago

























            answered 6 hours ago









            BigbearZzzBigbearZzz

            8,04821650




            8,04821650























                5












                $begingroup$

                There is basically no difference between mapping and function. In algebra, one uses the notion of operation which is the same as mapping or function. The notion of relation is more general. Functions are specific relations (those which are left-total and right-unique).






                share|cite|improve this answer









                $endgroup$


















                  5












                  $begingroup$

                  There is basically no difference between mapping and function. In algebra, one uses the notion of operation which is the same as mapping or function. The notion of relation is more general. Functions are specific relations (those which are left-total and right-unique).






                  share|cite|improve this answer









                  $endgroup$
















                    5












                    5








                    5





                    $begingroup$

                    There is basically no difference between mapping and function. In algebra, one uses the notion of operation which is the same as mapping or function. The notion of relation is more general. Functions are specific relations (those which are left-total and right-unique).






                    share|cite|improve this answer









                    $endgroup$



                    There is basically no difference between mapping and function. In algebra, one uses the notion of operation which is the same as mapping or function. The notion of relation is more general. Functions are specific relations (those which are left-total and right-unique).







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered 7 hours ago









                    WuestenfuxWuestenfux

                    3,9201411




                    3,9201411























                        0












                        $begingroup$

                        Relation and Function are quite different as the later only consider unique images.



                        There's not much difference between a mapping and function. The only difference that I can think of is that mapping is just the diagramatical representation of a function or an arrow diagram representation of a function which is quite clear for functions defined on the finite sets, while for infinite sets the two notions coincide.



                        I Hope it Helps...






                        share|cite|improve this answer









                        $endgroup$


















                          0












                          $begingroup$

                          Relation and Function are quite different as the later only consider unique images.



                          There's not much difference between a mapping and function. The only difference that I can think of is that mapping is just the diagramatical representation of a function or an arrow diagram representation of a function which is quite clear for functions defined on the finite sets, while for infinite sets the two notions coincide.



                          I Hope it Helps...






                          share|cite|improve this answer









                          $endgroup$
















                            0












                            0








                            0





                            $begingroup$

                            Relation and Function are quite different as the later only consider unique images.



                            There's not much difference between a mapping and function. The only difference that I can think of is that mapping is just the diagramatical representation of a function or an arrow diagram representation of a function which is quite clear for functions defined on the finite sets, while for infinite sets the two notions coincide.



                            I Hope it Helps...






                            share|cite|improve this answer









                            $endgroup$



                            Relation and Function are quite different as the later only consider unique images.



                            There's not much difference between a mapping and function. The only difference that I can think of is that mapping is just the diagramatical representation of a function or an arrow diagram representation of a function which is quite clear for functions defined on the finite sets, while for infinite sets the two notions coincide.



                            I Hope it Helps...







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 6 hours ago









                            Devendra Singh RanaDevendra Singh Rana

                            759416




                            759416






















                                user634631 is a new contributor. Be nice, and check out our Code of Conduct.










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                                user634631 is a new contributor. Be nice, and check out our Code of Conduct.













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