On notation of a linear algebra definition of a set of functions.

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I'm confused on a definition in my Linear Algebra textbook, Linear Algebra Done Right by Sheldon Axler.

If $S$ is a set, then $F^S$ denotes the set of functions from $S$ to $F$.

Specifically, I'm confused when the author says that the set of functions goes from $S$ to $F$. One of the points of confusion is what he means by "goes" and that $F$ is not defined to be a function, it's defined to be the set of every real or complex number, not a function. If $F$ does not contain functions, how can $F^S$ which is a set of functions be equal to $F$?

Will someone explain the definition more explicitly?

linear-algebra

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edited Jul 22 at 20:28

littleO

26.1k540101

asked Jul 22 at 20:18

Andrew Ferro

586

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It's better to write the text directly into the question, which makes the question searchable in the future and also makes the question easier to read.
  – littleO
  Jul 22 at 20:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I used Latex, is there a better way to write mathematical notation for stack exchange?
  – Andrew Ferro
  Jul 22 at 20:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It's good that you used Latex, but rather than posting an image of the question you can type the question here directly.
  – littleO
  Jul 22 at 20:22
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Note that in this context the capital $F$ stands for "field", not "function".
  – littleO
  Jul 22 at 20:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I went ahead and edited the question, you can take a look and see how MathJax is used when writing a question like this.
  – littleO
  Jul 22 at 20:30
  

  
  
  
  

 | 
show 3 more comments

up vote
-2
down vote

favorite

I'm confused on a definition in my Linear Algebra textbook, Linear Algebra Done Right by Sheldon Axler.

If $S$ is a set, then $F^S$ denotes the set of functions from $S$ to $F$.

Specifically, I'm confused when the author says that the set of functions goes from $S$ to $F$. One of the points of confusion is what he means by "goes" and that $F$ is not defined to be a function, it's defined to be the set of every real or complex number, not a function. If $F$ does not contain functions, how can $F^S$ which is a set of functions be equal to $F$?

Will someone explain the definition more explicitly?

linear-algebra

share|cite|improve this question

edited Jul 22 at 20:28

littleO

26.1k540101

asked Jul 22 at 20:18

Andrew Ferro

586

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It's better to write the text directly into the question, which makes the question searchable in the future and also makes the question easier to read.
  – littleO
  Jul 22 at 20:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I used Latex, is there a better way to write mathematical notation for stack exchange?
  – Andrew Ferro
  Jul 22 at 20:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It's good that you used Latex, but rather than posting an image of the question you can type the question here directly.
  – littleO
  Jul 22 at 20:22
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Note that in this context the capital $F$ stands for "field", not "function".
  – littleO
  Jul 22 at 20:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I went ahead and edited the question, you can take a look and see how MathJax is used when writing a question like this.
  – littleO
  Jul 22 at 20:30
  

  
  
  
  

 | 
show 3 more comments

up vote
-2
down vote

favorite

up vote
-2
down vote

favorite

I'm confused on a definition in my Linear Algebra textbook, Linear Algebra Done Right by Sheldon Axler.

If $S$ is a set, then $F^S$ denotes the set of functions from $S$ to $F$.

Specifically, I'm confused when the author says that the set of functions goes from $S$ to $F$. One of the points of confusion is what he means by "goes" and that $F$ is not defined to be a function, it's defined to be the set of every real or complex number, not a function. If $F$ does not contain functions, how can $F^S$ which is a set of functions be equal to $F$?

Will someone explain the definition more explicitly?

linear-algebra

share|cite|improve this question

edited Jul 22 at 20:28

littleO

26.1k540101

asked Jul 22 at 20:18

Andrew Ferro

586

I'm confused on a definition in my Linear Algebra textbook, Linear Algebra Done Right by Sheldon Axler.

If $S$ is a set, then $F^S$ denotes the set of functions from $S$ to $F$.

Specifically, I'm confused when the author says that the set of functions goes from $S$ to $F$. One of the points of confusion is what he means by "goes" and that $F$ is not defined to be a function, it's defined to be the set of every real or complex number, not a function. If $F$ does not contain functions, how can $F^S$ which is a set of functions be equal to $F$?

Will someone explain the definition more explicitly?

linear-algebra

share|cite|improve this question

edited Jul 22 at 20:28

littleO

26.1k540101

asked Jul 22 at 20:18

Andrew Ferro

586

share|cite|improve this question

share|cite|improve this question

edited Jul 22 at 20:28

littleO

26.1k540101

edited Jul 22 at 20:28

littleO

26.1k540101

edited Jul 22 at 20:28

littleO

26.1k540101

26.1k540101

asked Jul 22 at 20:18

Andrew Ferro

586

asked Jul 22 at 20:18

Andrew Ferro

586

asked Jul 22 at 20:18

Andrew Ferro

586

586

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It's better to write the text directly into the question, which makes the question searchable in the future and also makes the question easier to read.
  – littleO
  Jul 22 at 20:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I used Latex, is there a better way to write mathematical notation for stack exchange?
  – Andrew Ferro
  Jul 22 at 20:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It's good that you used Latex, but rather than posting an image of the question you can type the question here directly.
  – littleO
  Jul 22 at 20:22
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Note that in this context the capital $F$ stands for "field", not "function".
  – littleO
  Jul 22 at 20:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I went ahead and edited the question, you can take a look and see how MathJax is used when writing a question like this.
  – littleO
  Jul 22 at 20:30
  

  
  
  
  

 | 
show 3 more comments

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  It's better to write the text directly into the question, which makes the question searchable in the future and also makes the question easier to read.
  – littleO
  Jul 22 at 20:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I used Latex, is there a better way to write mathematical notation for stack exchange?
  – Andrew Ferro
  Jul 22 at 20:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It's good that you used Latex, but rather than posting an image of the question you can type the question here directly.
  – littleO
  Jul 22 at 20:22
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Note that in this context the capital $F$ stands for "field", not "function".
  – littleO
  Jul 22 at 20:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I went ahead and edited the question, you can take a look and see how MathJax is used when writing a question like this.
  – littleO
  Jul 22 at 20:30
  

  
  
  
  

1

1

It's better to write the text directly into the question, which makes the question searchable in the future and also makes the question easier to read.
– littleO
Jul 22 at 20:20

It's better to write the text directly into the question, which makes the question searchable in the future and also makes the question easier to read.
– littleO
Jul 22 at 20:20

I used Latex, is there a better way to write mathematical notation for stack exchange?
– Andrew Ferro
Jul 22 at 20:21

I used Latex, is there a better way to write mathematical notation for stack exchange?
– Andrew Ferro
Jul 22 at 20:21

It's good that you used Latex, but rather than posting an image of the question you can type the question here directly.
– littleO
Jul 22 at 20:22

It's good that you used Latex, but rather than posting an image of the question you can type the question here directly.
– littleO
Jul 22 at 20:22

Note that in this context the capital $F$ stands for "field", not "function".
– littleO
Jul 22 at 20:23

Note that in this context the capital $F$ stands for "field", not "function".
– littleO
Jul 22 at 20:23

I went ahead and edited the question, you can take a look and see how MathJax is used when writing a question like this.
– littleO
Jul 22 at 20:30

I went ahead and edited the question, you can take a look and see how MathJax is used when writing a question like this.
– littleO
Jul 22 at 20:30

 | 
show 3 more comments

2 Answers
2

active

oldest

votes

up vote
2
down vote

It means the set of function of the form $f:Sto F$, i.e., the set of functions whose domain is $S$ and their codomain is $F$.

share|cite|improve this answer

answered Jul 22 at 20:20

Javi

2,1631725

add a comment | 

up vote
0
down vote

I have just looked this up in Linear Algebra Done Right, Chapter#1 page 14. $mathbfF^S$ denotes the set of all functions from $mathbfF$ to $S$ formally speaking we have
$$mathbfF^S = h:StomathbfF$$

where $F$ is the field of either the set of all real numbers or the set of all complex numbers.

share|cite|improve this answer

answered Jul 22 at 21:17

Atif Farooq

2,7092824

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Not seeing this was a failure of my ability to interpret context.
  – Andrew Ferro
  Jul 23 at 0:16
  

  
  
  
  

add a comment | 

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

It means the set of function of the form $f:Sto F$, i.e., the set of functions whose domain is $S$ and their codomain is $F$.

share|cite|improve this answer

answered Jul 22 at 20:20

Javi

2,1631725

add a comment | 

up vote
2
down vote

It means the set of function of the form $f:Sto F$, i.e., the set of functions whose domain is $S$ and their codomain is $F$.

share|cite|improve this answer

answered Jul 22 at 20:20

Javi

2,1631725

add a comment | 

up vote
2
down vote

up vote
2
down vote

It means the set of function of the form $f:Sto F$, i.e., the set of functions whose domain is $S$ and their codomain is $F$.

share|cite|improve this answer

answered Jul 22 at 20:20

Javi

2,1631725

It means the set of function of the form $f:Sto F$, i.e., the set of functions whose domain is $S$ and their codomain is $F$.

share|cite|improve this answer

answered Jul 22 at 20:20

Javi

2,1631725

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 20:20

Javi

2,1631725

answered Jul 22 at 20:20

Javi

2,1631725

answered Jul 22 at 20:20

Javi

2,1631725

2,1631725

add a comment | 

add a comment | 

up vote
0
down vote

I have just looked this up in Linear Algebra Done Right, Chapter#1 page 14. $mathbfF^S$ denotes the set of all functions from $mathbfF$ to $S$ formally speaking we have
$$mathbfF^S = h:StomathbfF$$

where $F$ is the field of either the set of all real numbers or the set of all complex numbers.

share|cite|improve this answer

answered Jul 22 at 21:17

Atif Farooq

2,7092824

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Not seeing this was a failure of my ability to interpret context.
  – Andrew Ferro
  Jul 23 at 0:16
  

  
  
  
  

add a comment | 

up vote
0
down vote

I have just looked this up in Linear Algebra Done Right, Chapter#1 page 14. $mathbfF^S$ denotes the set of all functions from $mathbfF$ to $S$ formally speaking we have
$$mathbfF^S = h:StomathbfF$$

where $F$ is the field of either the set of all real numbers or the set of all complex numbers.

share|cite|improve this answer

answered Jul 22 at 21:17

Atif Farooq

2,7092824

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Not seeing this was a failure of my ability to interpret context.
  – Andrew Ferro
  Jul 23 at 0:16
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

I have just looked this up in Linear Algebra Done Right, Chapter#1 page 14. $mathbfF^S$ denotes the set of all functions from $mathbfF$ to $S$ formally speaking we have
$$mathbfF^S = h:StomathbfF$$

where $F$ is the field of either the set of all real numbers or the set of all complex numbers.

share|cite|improve this answer

answered Jul 22 at 21:17

Atif Farooq

2,7092824

I have just looked this up in Linear Algebra Done Right, Chapter#1 page 14. $mathbfF^S$ denotes the set of all functions from $mathbfF$ to $S$ formally speaking we have
$$mathbfF^S = h:StomathbfF$$

where $F$ is the field of either the set of all real numbers or the set of all complex numbers.

share|cite|improve this answer

answered Jul 22 at 21:17

Atif Farooq

2,7092824

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 21:17

Atif Farooq

2,7092824

answered Jul 22 at 21:17

Atif Farooq

2,7092824

answered Jul 22 at 21:17

Atif Farooq

2,7092824

2,7092824

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Not seeing this was a failure of my ability to interpret context.
  – Andrew Ferro
  Jul 23 at 0:16
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Not seeing this was a failure of my ability to interpret context.
  – Andrew Ferro
  Jul 23 at 0:16
  

  
  
  
  

1

1

Not seeing this was a failure of my ability to interpret context.
– Andrew Ferro
Jul 23 at 0:16

Not seeing this was a failure of my ability to interpret context.
– Andrew Ferro
Jul 23 at 0:16

add a comment | 

 

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