What does H represent in the graph of y = 2H(x - 4)?

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Discussion Overview

The discussion revolves around the interpretation of the variable "H" in the mathematical expression y = 2H(x - 4). Participants are exploring the nature of the function H, particularly in the context of the Heaviside step function, and how it affects the graphing of the equation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the meaning of "H" and whether it represents a specific constant.
  • Another participant suggests that "H" likely refers to the Heaviside step function, providing a link for reference.
  • A participant points out discrepancies in the definitions of the Heaviside function found in different sources, specifically regarding the value of H(0).
  • Some participants discuss the historical context of the definitions of H(0), noting that one definition assigns H(0) = 0 while another assigns H(0) = 1/2.
  • There is a mention that the choice of definition for H(0) may not significantly impact applications in particle physics.
  • One participant proposes that using an approximation like a Fourier series could justify defining H(0) as 1/2 due to the Gibbs phenomenon.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate definition of the Heaviside function, particularly at the point H(0). There is no consensus on which definition should be followed.

Contextual Notes

The discussion highlights the ambiguity in the definition of the Heaviside step function and its implications for graphing the given equation. The historical context of the definitions may influence their applicability in various fields.

jaja1990
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What does "H" mean?!

I have this question in my assignment paper:-

8. Sketch the graph of:
(a)
y = |2x − 2|;
(b)
y = 2H(x − 4)

(a) is obvious, but how do I sketch (b)? Does "H" stand for some specific constant?
 
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The webpage in the link you've given says:-
The function is:-
0 when x < 0,
1/2 when x = 0,
1 when x > 0.
But here: http://simple.wikipedia.org/wiki/Heaviside_Function, defines the function as:-
1 when x => 0,
0 when x < 0.

To begin with, which should I follow?
 


I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in particle applications.
 


JJacquelin said:
I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in particle applications.

If one wanted to use an approximation like a Fourier series version, then it makes sense to define H(0) as 1/2 based on properties of Fourier series when you have this kind of 'Gibbs' phenomenon.
 

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