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How to express a function mapping an integer to the multiple $3$-dimensional space?
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I want to define a function $f$ mapping an integer $n$ to $underbracemathbbR^3timesmathbbR^3_n$.
Is it correct to express the function $f$ as
$$
f : mathbbN to mathbbR^3timesmathbbN ~ ?
$$
For me, it is some weird. I want to define a function $f:nmapstomathbbR^n$ in a form of domain to domain. Is there a way to express the function $f$ well?
For example, $f(3)$ gives three $3$-vectors, $f(10)$ gives ten $3$-vectors, and so forth, where the $3$-vector implies a vector having $3$ elements.
For a detail example, $f(2)=(1,2,3), (10,5,3)$.
functions notation
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
asked Jul 23 at 14:17
Danny_Kim
1,3211620
add a comment |Â
up vote
0
down vote
favorite
I want to define a function $f$ mapping an integer $n$ to $underbracemathbbR^3timesmathbbR^3_n$.
Is it correct to express the function $f$ as
$$
f : mathbbN to mathbbR^3timesmathbbN ~ ?
$$
For me, it is some weird. I want to define a function $f:nmapstomathbbR^n$ in a form of domain to domain. Is there a way to express the function $f$ well?
For example, $f(3)$ gives three $3$-vectors, $f(10)$ gives ten $3$-vectors, and so forth, where the $3$-vector implies a vector having $3$ elements.
For a detail example, $f(2)=(1,2,3), (10,5,3)$.
functions notation
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
asked Jul 23 at 14:17
Danny_Kim
1,3211620
Your question is a little confusing. Can you give a specific example of input values and output values of the question? For example, what might the values of $f(1)$ and $f(2)$ and $f(7)$ be for your function?
– Lee Mosher
Jul 23 at 14:19
What does $underbracemathbbR^3timesmathbbR^3_n$ even mean?
– Asaf Karagila
Jul 23 at 14:21
A simple definition is $nmapsto (n,n,n,ldots ,n,n,n)$.
– Dietrich Burde
Jul 23 at 14:21
@LeeMosher, Asaf Karagila I edited my question.
– Danny_Kim
Jul 23 at 14:21
@DietrichBurde Is it fine if I define a function by an element in domain $mapsto$ element in range, rather than domain $to$ codomain?
– Danny_Kim
Jul 23 at 14:23
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I want to define a function $f$ mapping an integer $n$ to $underbracemathbbR^3timesmathbbR^3_n$.
Is it correct to express the function $f$ as
$$
f : mathbbN to mathbbR^3timesmathbbN ~ ?
$$
For me, it is some weird. I want to define a function $f:nmapstomathbbR^n$ in a form of domain to domain. Is there a way to express the function $f$ well?
For example, $f(3)$ gives three $3$-vectors, $f(10)$ gives ten $3$-vectors, and so forth, where the $3$-vector implies a vector having $3$ elements.
For a detail example, $f(2)=(1,2,3), (10,5,3)$.
functions notation
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
asked Jul 23 at 14:17
Danny_Kim
1,3211620
I want to define a function $f$ mapping an integer $n$ to $underbracemathbbR^3timesmathbbR^3_n$.
Is it correct to express the function $f$ as
$$
f : mathbbN to mathbbR^3timesmathbbN ~ ?
$$
For me, it is some weird. I want to define a function $f:nmapstomathbbR^n$ in a form of domain to domain. Is there a way to express the function $f$ well?
For example, $f(3)$ gives three $3$-vectors, $f(10)$ gives ten $3$-vectors, and so forth, where the $3$-vector implies a vector having $3$ elements.
For a detail example, $f(2)=(1,2,3), (10,5,3)$.
functions notation
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
asked Jul 23 at 14:17
Danny_Kim
1,3211620
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
edited Jul 23 at 14:26
J.-E. Pin
16.6k21751
16.6k21751
asked Jul 23 at 14:17
Danny_Kim
1,3211620
asked Jul 23 at 14:17
Danny_Kim
1,3211620
asked Jul 23 at 14:17
Danny_Kim
1,3211620
1,3211620
Your question is a little confusing. Can you give a specific example of input values and output values of the question? For example, what might the values of $f(1)$ and $f(2)$ and $f(7)$ be for your function?
– Lee Mosher
Jul 23 at 14:19
What does $underbracemathbbR^3timesmathbbR^3_n$ even mean?
– Asaf Karagila
Jul 23 at 14:21
A simple definition is $nmapsto (n,n,n,ldots ,n,n,n)$.
– Dietrich Burde
Jul 23 at 14:21
@LeeMosher, Asaf Karagila I edited my question.
– Danny_Kim
Jul 23 at 14:21
@DietrichBurde Is it fine if I define a function by an element in domain $mapsto$ element in range, rather than domain $to$ codomain?
– Danny_Kim
Jul 23 at 14:23
add a comment |Â
Your question is a little confusing. Can you give a specific example of input values and output values of the question? For example, what might the values of $f(1)$ and $f(2)$ and $f(7)$ be for your function?
– Lee Mosher
Jul 23 at 14:19
What does $underbracemathbbR^3timesmathbbR^3_n$ even mean?
– Asaf Karagila
Jul 23 at 14:21
A simple definition is $nmapsto (n,n,n,ldots ,n,n,n)$.
– Dietrich Burde
Jul 23 at 14:21
@LeeMosher, Asaf Karagila I edited my question.
– Danny_Kim
Jul 23 at 14:21
@DietrichBurde Is it fine if I define a function by an element in domain $mapsto$ element in range, rather than domain $to$ codomain?
– Danny_Kim
Jul 23 at 14:23
Your question is a little confusing. Can you give a specific example of input values and output values of the question? For example, what might the values of $f(1)$ and $f(2)$ and $f(7)$ be for your function?
– Lee Mosher
Jul 23 at 14:19
Your question is a little confusing. Can you give a specific example of input values and output values of the question? For example, what might the values of $f(1)$ and $f(2)$ and $f(7)$ be for your function?
– Lee Mosher
Jul 23 at 14:19
What does $underbracemathbbR^3timesmathbbR^3_n$ even mean?
– Asaf Karagila
Jul 23 at 14:21
What does $underbracemathbbR^3timesmathbbR^3_n$ even mean?
– Asaf Karagila
Jul 23 at 14:21
A simple definition is $nmapsto (n,n,n,ldots ,n,n,n)$.
– Dietrich Burde
Jul 23 at 14:21
A simple definition is $nmapsto (n,n,n,ldots ,n,n,n)$.
– Dietrich Burde
Jul 23 at 14:21
@LeeMosher, Asaf Karagila I edited my question.
– Danny_Kim
Jul 23 at 14:21
@LeeMosher, Asaf Karagila I edited my question.
– Danny_Kim
Jul 23 at 14:21
@DietrichBurde Is it fine if I define a function by an element in domain $mapsto$ element in range, rather than domain $to$ codomain?
– Danny_Kim
Jul 23 at 14:23
@DietrichBurde Is it fine if I define a function by an element in domain $mapsto$ element in range, rather than domain $to$ codomain?
– Danny_Kim
Jul 23 at 14:23
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
Well, that depends on how you want to treat things.
In general, you can talk about $X^<Bbb N$ as the collection of finite sequences from $X$, which then you can choose to formalize as a subset of $X^Bbb N$ where every function is eventually $0$ (you can even declare the first coordinate of each function as "its length", to avoid confusion (although it might introduce other difficulties).
So it seems to me that $fcolonBbbNto(R^3)^<N$.
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Well, that depends on how you want to treat things.
In general, you can talk about $X^<Bbb N$ as the collection of finite sequences from $X$, which then you can choose to formalize as a subset of $X^Bbb N$ where every function is eventually $0$ (you can even declare the first coordinate of each function as "its length", to avoid confusion (although it might introduce other difficulties).
So it seems to me that $fcolonBbbNto(R^3)^<N$.
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
add a comment |Â
up vote
0
down vote
accepted
Well, that depends on how you want to treat things.
In general, you can talk about $X^<Bbb N$ as the collection of finite sequences from $X$, which then you can choose to formalize as a subset of $X^Bbb N$ where every function is eventually $0$ (you can even declare the first coordinate of each function as "its length", to avoid confusion (although it might introduce other difficulties).
So it seems to me that $fcolonBbbNto(R^3)^<N$.
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Well, that depends on how you want to treat things.
In general, you can talk about $X^<Bbb N$ as the collection of finite sequences from $X$, which then you can choose to formalize as a subset of $X^Bbb N$ where every function is eventually $0$ (you can even declare the first coordinate of each function as "its length", to avoid confusion (although it might introduce other difficulties).
So it seems to me that $fcolonBbbNto(R^3)^<N$.
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
Well, that depends on how you want to treat things.
In general, you can talk about $X^<Bbb N$ as the collection of finite sequences from $X$, which then you can choose to formalize as a subset of $X^Bbb N$ where every function is eventually $0$ (you can even declare the first coordinate of each function as "its length", to avoid confusion (although it might introduce other difficulties).
So it seems to me that $fcolonBbbNto(R^3)^<N$.
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
answered Jul 23 at 14:25
Asaf Karagila
291k31402732
291k31402732
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
add a comment |Â
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
I first noticed the notation like $(mathbbR^3)^<mathbbN$, thank you.
– Danny_Kim
Jul 23 at 14:27
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
The standard notation in theoretical computer science and in semigroup theory is $X^*$ (the free monoid of base $X$), but in this context you may have to explain this notation to avoid any confusion with dual spaces.
– J.-E. Pin
Jul 23 at 16:19
add a comment |Â
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Your question is a little confusing. Can you give a specific example of input values and output values of the question? For example, what might the values of $f(1)$ and $f(2)$ and $f(7)$ be for your function?
– Lee Mosher
Jul 23 at 14:19
What does $underbracemathbbR^3timesmathbbR^3_n$ even mean?
– Asaf Karagila
Jul 23 at 14:21
A simple definition is $nmapsto (n,n,n,ldots ,n,n,n)$.
– Dietrich Burde
Jul 23 at 14:21
@LeeMosher, Asaf Karagila I edited my question.
– Danny_Kim
Jul 23 at 14:21
@DietrichBurde Is it fine if I define a function by an element in domain $mapsto$ element in range, rather than domain $to$ codomain?
– Danny_Kim
Jul 23 at 14:23