What do we call the restriction of some function to a certain domain?
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
asked Apr 13 '17 at 12:36
user334732
4,23111240
add a comment |
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
asked Apr 13 '17 at 12:36
user334732
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
add a comment |
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
asked Apr 13 '17 at 12:36
user334732
4,23111240
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
asked Apr 13 '17 at 12:36
user334732
4,23111240
asked Apr 13 '17 at 12:36
user334732
4,23111240
asked Apr 13 '17 at 12:36
user334732
4,23111240
asked Apr 13 '17 at 12:36
user334732
4,23111240
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
add a comment |
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
add a comment |
1 Answer
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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 "$f(a)$".)
answered Nov 25 at 14:27
Mark S.
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
add a comment |
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1 Answer
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1 Answer
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active
oldest
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oldest
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active
oldest
votes
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 "$f(a)$".)
answered Nov 25 at 14:27
Mark S.
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
add a comment |
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 "$f(a)$".)
answered Nov 25 at 14:27
Mark S.
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
add a comment |
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 "$f(a)$".)
answered Nov 25 at 14:27
Mark S.
11.7k22669
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 "$f(a)$".)
answered Nov 25 at 14:27
Mark S.
11.7k22669
answered Nov 25 at 14:27
Mark S.
11.7k22669
answered Nov 25 at 14:27
Mark S.
11.7k22669
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
add a comment |
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
add a comment |
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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