What do we call the restriction of some function to a certain domain?












2














What do we call the restriction of some function to a certain subset of its domain and range?



Suppose some function $g:mathbb{Q}tomathbb{Q}$ is an extension of a function $f:mathbb{N}tomathbb{N}$.



Is there a term for $g$ restricted to $mathbb{N}$?






notation terminology







share|cite|improve this question


















  • 2




    I'm not sure I understand the question. It seems like the answer is "yes, the word you used, 'restriction', is the term for the thing you called a 'restriction'."
    – Mark S.
    Apr 13 '17 at 12:51






  • 2




    It's common to see exactly what you've written: $g$ restricted to $mathbb N$, but in most cases the restriction on the range is not written.
    – dannum
    Apr 13 '17 at 13:22


















2














What do we call the restriction of some function to a certain subset of its domain and range?



Suppose some function $g:mathbb{Q}tomathbb{Q}$ is an extension of a function $f:mathbb{N}tomathbb{N}$.



Is there a term for $g$ restricted to $mathbb{N}$?






notation terminology







share|cite|improve this question


















  • 2




    I'm not sure I understand the question. It seems like the answer is "yes, the word you used, 'restriction', is the term for the thing you called a 'restriction'."
    – Mark S.
    Apr 13 '17 at 12:51






  • 2




    It's common to see exactly what you've written: $g$ restricted to $mathbb N$, but in most cases the restriction on the range is not written.
    – dannum
    Apr 13 '17 at 13:22
















2












2








2







What do we call the restriction of some function to a certain subset of its domain and range?



Suppose some function $g:mathbb{Q}tomathbb{Q}$ is an extension of a function $f:mathbb{N}tomathbb{N}$.



Is there a term for $g$ restricted to $mathbb{N}$?






notation terminology







share|cite|improve this question













What do we call the restriction of some function to a certain subset of its domain and range?



Suppose some function $g:mathbb{Q}tomathbb{Q}$ is an extension of a function $f:mathbb{N}tomathbb{N}$.



Is there a term for $g$ restricted to $mathbb{N}$?






notation terminology




notation terminology






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Apr 13 '17 at 12:36









user334732

4,23111240




4,23111240








  • 2




    I'm not sure I understand the question. It seems like the answer is "yes, the word you used, 'restriction', is the term for the thing you called a 'restriction'."
    – Mark S.
    Apr 13 '17 at 12:51






  • 2




    It's common to see exactly what you've written: $g$ restricted to $mathbb N$, but in most cases the restriction on the range is not written.
    – dannum
    Apr 13 '17 at 13:22
















  • 2




    I'm not sure I understand the question. It seems like the answer is "yes, the word you used, 'restriction', is the term for the thing you called a 'restriction'."
    – Mark S.
    Apr 13 '17 at 12:51






  • 2




    It's common to see exactly what you've written: $g$ restricted to $mathbb N$, but in most cases the restriction on the range is not written.
    – dannum
    Apr 13 '17 at 13:22










2




2




I'm not sure I understand the question. It seems like the answer is "yes, the word you used, 'restriction', is the term for the thing you called a 'restriction'."
– Mark S.
Apr 13 '17 at 12:51




I'm not sure I understand the question. It seems like the answer is "yes, the word you used, 'restriction', is the term for the thing you called a 'restriction'."
– Mark S.
Apr 13 '17 at 12:51




2




2




It's common to see exactly what you've written: $g$ restricted to $mathbb N$, but in most cases the restriction on the range is not written.
– dannum
Apr 13 '17 at 13:22






It's common to see exactly what you've written: $g$ restricted to $mathbb N$, but in most cases the restriction on the range is not written.
– dannum
Apr 13 '17 at 13:22












1 Answer
1






active

oldest

votes


















1














As Wikipedia implies, I believe "restriction (of a function)" is most commonly used to modify the domain only. Without context suggesting otherwise, I would interpret "$g$ restricted to $mathbb N$" as meaning a function $f:mathbb Ntomathbb Q$ with $f(n)=g(n)$ for all $nin mathbb N$.



However, there is precedent for using the word "restriction" to refer to modifying the codomain or both. A part of the same wikipedia page talks about "left-restrictions" and "right-restrictions" for the two sets.



For a text reference, Topology and Groupoids by Ronald Brown explicitly calls modifying both a restriction. In the book's notation, if $f:Ato B$, $A'subseteq A$, $B'subseteq B$, and $f(a)in B'$ for all $ain A'$ then $fmid A',B'$ is the restriction of $f$ which maps $A'to B'$. (Well, the book writes "$fa$" in where I wrote "$f(a)$".)






share|cite|improve this answer





















  • I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
    – user334732
    Nov 26 at 2:07






  • 1




    @RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
    – Mark S.
    Nov 26 at 2:22











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1 Answer
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active

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1














As Wikipedia implies, I believe "restriction (of a function)" is most commonly used to modify the domain only. Without context suggesting otherwise, I would interpret "$g$ restricted to $mathbb N$" as meaning a function $f:mathbb Ntomathbb Q$ with $f(n)=g(n)$ for all $nin mathbb N$.



However, there is precedent for using the word "restriction" to refer to modifying the codomain or both. A part of the same wikipedia page talks about "left-restrictions" and "right-restrictions" for the two sets.



For a text reference, Topology and Groupoids by Ronald Brown explicitly calls modifying both a restriction. In the book's notation, if $f:Ato B$, $A'subseteq A$, $B'subseteq B$, and $f(a)in B'$ for all $ain A'$ then $fmid A',B'$ is the restriction of $f$ which maps $A'to B'$. (Well, the book writes "$fa$" in where I wrote "$f(a)$".)






share|cite|improve this answer





















  • I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
    – user334732
    Nov 26 at 2:07






  • 1




    @RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
    – Mark S.
    Nov 26 at 2:22
















1














As Wikipedia implies, I believe "restriction (of a function)" is most commonly used to modify the domain only. Without context suggesting otherwise, I would interpret "$g$ restricted to $mathbb N$" as meaning a function $f:mathbb Ntomathbb Q$ with $f(n)=g(n)$ for all $nin mathbb N$.



However, there is precedent for using the word "restriction" to refer to modifying the codomain or both. A part of the same wikipedia page talks about "left-restrictions" and "right-restrictions" for the two sets.



For a text reference, Topology and Groupoids by Ronald Brown explicitly calls modifying both a restriction. In the book's notation, if $f:Ato B$, $A'subseteq A$, $B'subseteq B$, and $f(a)in B'$ for all $ain A'$ then $fmid A',B'$ is the restriction of $f$ which maps $A'to B'$. (Well, the book writes "$fa$" in where I wrote "$f(a)$".)






share|cite|improve this answer





















  • I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
    – user334732
    Nov 26 at 2:07






  • 1




    @RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
    – Mark S.
    Nov 26 at 2:22














1












1








1






As Wikipedia implies, I believe "restriction (of a function)" is most commonly used to modify the domain only. Without context suggesting otherwise, I would interpret "$g$ restricted to $mathbb N$" as meaning a function $f:mathbb Ntomathbb Q$ with $f(n)=g(n)$ for all $nin mathbb N$.



However, there is precedent for using the word "restriction" to refer to modifying the codomain or both. A part of the same wikipedia page talks about "left-restrictions" and "right-restrictions" for the two sets.



For a text reference, Topology and Groupoids by Ronald Brown explicitly calls modifying both a restriction. In the book's notation, if $f:Ato B$, $A'subseteq A$, $B'subseteq B$, and $f(a)in B'$ for all $ain A'$ then $fmid A',B'$ is the restriction of $f$ which maps $A'to B'$. (Well, the book writes "$fa$" in where I wrote "$f(a)$".)






share|cite|improve this answer












As Wikipedia implies, I believe "restriction (of a function)" is most commonly used to modify the domain only. Without context suggesting otherwise, I would interpret "$g$ restricted to $mathbb N$" as meaning a function $f:mathbb Ntomathbb Q$ with $f(n)=g(n)$ for all $nin mathbb N$.



However, there is precedent for using the word "restriction" to refer to modifying the codomain or both. A part of the same wikipedia page talks about "left-restrictions" and "right-restrictions" for the two sets.



For a text reference, Topology and Groupoids by Ronald Brown explicitly calls modifying both a restriction. In the book's notation, if $f:Ato B$, $A'subseteq A$, $B'subseteq B$, and $f(a)in B'$ for all $ain A'$ then $fmid A',B'$ is the restriction of $f$ which maps $A'to B'$. (Well, the book writes "$fa$" in where I wrote "$f(a)$".)







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 25 at 14:27









Mark S.

11.7k22669




11.7k22669












  • I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
    – user334732
    Nov 26 at 2:07






  • 1




    @RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
    – Mark S.
    Nov 26 at 2:22


















  • I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
    – user334732
    Nov 26 at 2:07






  • 1




    @RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
    – Mark S.
    Nov 26 at 2:22
















I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
– user334732
Nov 26 at 2:07




I'm interpreting $fa$ to be pretty much interchangeable with $f(a)$ when getting into groups in which composition is the group operation? Rather than a typo.
– user334732
Nov 26 at 2:07




1




1




@RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
– Mark S.
Nov 26 at 2:22




@RobertFrost Well, we don't have to talk about it from a group perspective, per se, but yes, it's not a typo - that book just drops parentheses for arguments of functions.
– Mark S.
Nov 26 at 2:22


















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