How to Denote a Restricted Function?

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Discussion Overview

The discussion revolves around how to denote a restricted function, specifically focusing on the notation used to express a function that is limited to a certain subset of its domain, such as the positive semi-axis.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks how to denote a restricted function, specifically seeking a concise notation for a function defined only on the positive semi-axis.
  • Another participant suggests that the function can be expressed as f(x) = F(x) for positive real numbers x, indicating a straightforward approach.
  • A third participant introduces the notation f|_S as the standard way to denote the restriction of a function to a subset S of its domain.
  • A later reply acknowledges the notation f|_S as the desired solution, expressing gratitude for the clarification.

Areas of Agreement / Disagreement

Participants generally agree on the notation f|_S as a standard method for denoting restricted functions, but there is no explicit consensus on the most concise way to express the restriction in the context of the original question.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the definitions of the functions or the subsets involved.

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How does one denote a restricted function?

For example, suppose I have a function [itex]F : \mathbb{R}\to\mathbb{R}[/itex], how would I denote a new function f, such that f is the restriction of F to the positive semi-axis? Up until this point I would have just said that f is the restriction of F to the positive semi-axis, but it occurs to me that there should be a more concise way of writing it.
 
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f(x)=F(x) for only x positive real number, there's not a lot about it.
 


[tex]f\vert_S[/tex] is the standard notation for the restriction of f to a subset S of f's domain.
 


Tac-Tics said:
[tex]f\vert_S[/tex] is the standard notation for the restriction of f to a subset S of f's domain.
That's exactly was I was looking for Tac-Tics.

Thanks to you both.
 

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