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Understanding the meaning of a function [duplicate]

0

$begingroup$

This question already has an answer here:

• 
  What is a function?
  
  10 answers
  
  

I am confused as to what really a function is ?

1. Is a function the steps by which we get the output from an input ?


2. Or is it the name of the process by which we get the output from an input ?

functions

share|cite|improve this question

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

$endgroup$

marked as duplicate by Eevee Trainer, drhab, Carl Christian, Michael Hoppe, Parcly Taxel Mar 21 at 0:57

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm pretty sure that this exact question has been already asked here ...
  $endgroup$
  – Matti P.
  Mar 20 at 9:16
  

  
  
  
  

add a comment | 

0

$begingroup$

This question already has an answer here:

• 
  What is a function?
  
  10 answers
  
  

I am confused as to what really a function is ?

1. Is a function the steps by which we get the output from an input ?


2. Or is it the name of the process by which we get the output from an input ?

functions

share|cite|improve this question

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

$endgroup$

marked as duplicate by Eevee Trainer, drhab, Carl Christian, Michael Hoppe, Parcly Taxel Mar 21 at 0:57

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm pretty sure that this exact question has been already asked here ...
  $endgroup$
  – Matti P.
  Mar 20 at 9:16
  

  
  
  
  

add a comment | 

$begingroup$

This question already has an answer here:

• 
  What is a function?
  
  10 answers
  
  

I am confused as to what really a function is ?

1. Is a function the steps by which we get the output from an input ?


2. Or is it the name of the process by which we get the output from an input ?

functions

share|cite|improve this question

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

$endgroup$

share|cite|improve this question

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

share|cite|improve this question

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

asked Mar 20 at 9:06

Ashok SharmaAshok Sharma

111

2 Answers
2

active

oldest

votes

0

$begingroup$

Simply put, a function is basically the description or the rule of the dependence of the output on the input. It may also be seen as a mapping of the set $X$ - the domain to the set $Y$- the codomain. Notation-aly $f: Xmapsto Y$.

Take the example of $f(x)=x^2$. Let $X$ be the set of Real Numbers denoted $mathbbR$. Clearly you can observe from the graph of $y=x^2$ that $f$ maps the input that is the real line to the positive real plane including $y=0$. Again, Notation-aly $f(x)=x^2 mid f:mathbbRmapsto mathbbR^+cup 0$.

I would suggest you consult Wikipedia's page on Functions for deeper detail.

share|cite|improve this answer

edited Mar 20 at 9:21

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You didn't make precise what you mean with "the description or the rule". Note that two functions can be equal, but have different "descriptions". Furthermore, not every function needs to have a "concrete" rule. Just imagine the choice-function provided by the axiom of choice. Typically, there is no "description or rule" for the function.
  $endgroup$
  – Babelfish
  Mar 20 at 10:20
  

  
  
  
  

add a comment | 

-1

$begingroup$

Consider the function $xmapsto x^2$. That describes the steps from input to output. Now you may refer to that function by a name, say $f$, so you write $fcolon xmapsto x^2$

share|cite|improve this answer

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why the downvote? Did I misunderstand the question?
  $endgroup$
  – Michael Hoppe
  Mar 20 at 12:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I downvoted your reply for two reasons. Firstly, because it did not address the real question, i.e., what is a function. Secondly, because your decision not to involve the domain and the codomain in the discussion, will in my opinion, push the OP in the wrong direction. I think that very basic questions should be answered at length.
  $endgroup$
  – Carl Christian
  Mar 20 at 21:24
  

  
  
  
  

add a comment | 

0

$begingroup$

Simply put, a function is basically the description or the rule of the dependence of the output on the input. It may also be seen as a mapping of the set $X$ - the domain to the set $Y$- the codomain. Notation-aly $f: Xmapsto Y$.

Take the example of $f(x)=x^2$. Let $X$ be the set of Real Numbers denoted $mathbbR$. Clearly you can observe from the graph of $y=x^2$ that $f$ maps the input that is the real line to the positive real plane including $y=0$. Again, Notation-aly $f(x)=x^2 mid f:mathbbRmapsto mathbbR^+cup 0$.

I would suggest you consult Wikipedia's page on Functions for deeper detail.

share|cite|improve this answer

edited Mar 20 at 9:21

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You didn't make precise what you mean with "the description or the rule". Note that two functions can be equal, but have different "descriptions". Furthermore, not every function needs to have a "concrete" rule. Just imagine the choice-function provided by the axiom of choice. Typically, there is no "description or rule" for the function.
  $endgroup$
  – Babelfish
  Mar 20 at 10:20
  

  
  
  
  

add a comment | 

0

$begingroup$

Simply put, a function is basically the description or the rule of the dependence of the output on the input. It may also be seen as a mapping of the set $X$ - the domain to the set $Y$- the codomain. Notation-aly $f: Xmapsto Y$.

Take the example of $f(x)=x^2$. Let $X$ be the set of Real Numbers denoted $mathbbR$. Clearly you can observe from the graph of $y=x^2$ that $f$ maps the input that is the real line to the positive real plane including $y=0$. Again, Notation-aly $f(x)=x^2 mid f:mathbbRmapsto mathbbR^+cup 0$.

I would suggest you consult Wikipedia's page on Functions for deeper detail.

share|cite|improve this answer

edited Mar 20 at 9:21

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You didn't make precise what you mean with "the description or the rule". Note that two functions can be equal, but have different "descriptions". Furthermore, not every function needs to have a "concrete" rule. Just imagine the choice-function provided by the axiom of choice. Typically, there is no "description or rule" for the function.
  $endgroup$
  – Babelfish
  Mar 20 at 10:20
  

  
  
  
  

add a comment | 

$begingroup$

Simply put, a function is basically the description or the rule of the dependence of the output on the input. It may also be seen as a mapping of the set $X$ - the domain to the set $Y$- the codomain. Notation-aly $f: Xmapsto Y$.

Take the example of $f(x)=x^2$. Let $X$ be the set of Real Numbers denoted $mathbbR$. Clearly you can observe from the graph of $y=x^2$ that $f$ maps the input that is the real line to the positive real plane including $y=0$. Again, Notation-aly $f(x)=x^2 mid f:mathbbRmapsto mathbbR^+cup 0$.

I would suggest you consult Wikipedia's page on Functions for deeper detail.

share|cite|improve this answer

edited Mar 20 at 9:21

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

$endgroup$

share|cite|improve this answer

edited Mar 20 at 9:21

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

answered Mar 20 at 9:16

Paras KhoslaParas Khosla

2,758423

-1

$begingroup$

Consider the function $xmapsto x^2$. That describes the steps from input to output. Now you may refer to that function by a name, say $f$, so you write $fcolon xmapsto x^2$

share|cite|improve this answer

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why the downvote? Did I misunderstand the question?
  $endgroup$
  – Michael Hoppe
  Mar 20 at 12:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I downvoted your reply for two reasons. Firstly, because it did not address the real question, i.e., what is a function. Secondly, because your decision not to involve the domain and the codomain in the discussion, will in my opinion, push the OP in the wrong direction. I think that very basic questions should be answered at length.
  $endgroup$
  – Carl Christian
  Mar 20 at 21:24
  

  
  
  
  

add a comment | 

-1

$begingroup$

Consider the function $xmapsto x^2$. That describes the steps from input to output. Now you may refer to that function by a name, say $f$, so you write $fcolon xmapsto x^2$

share|cite|improve this answer

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why the downvote? Did I misunderstand the question?
  $endgroup$
  – Michael Hoppe
  Mar 20 at 12:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I downvoted your reply for two reasons. Firstly, because it did not address the real question, i.e., what is a function. Secondly, because your decision not to involve the domain and the codomain in the discussion, will in my opinion, push the OP in the wrong direction. I think that very basic questions should be answered at length.
  $endgroup$
  – Carl Christian
  Mar 20 at 21:24
  

  
  
  
  

add a comment | 

$begingroup$

Consider the function $xmapsto x^2$. That describes the steps from input to output. Now you may refer to that function by a name, say $f$, so you write $fcolon xmapsto x^2$

share|cite|improve this answer

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837

$endgroup$

share|cite|improve this answer

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837

answered Mar 20 at 9:11

Michael HoppeMichael Hoppe

11.2k31837