Why are certain transformations in the case of D4 group considered even or odd?

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Discussion Overview

The discussion centers on the classification of transformations within the D4 group, specifically why certain transformations, such as ##\rho,\rho^2,\rho^3,\rho^4##, are considered even, while others, like ##\rho\sigma,\rho^2\sigma,\rho^3\sigma##, are classified as odd. The conversation seeks to clarify the definitions and implications of these classifications.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the classification of transformations as even or odd and seeks clarification on the definitions involved.
  • Another participant emphasizes the importance of understanding the definitions of "even" and "odd" transformations to engage meaningfully with the topic.
  • A further contribution suggests that without a clear definition, it is challenging to comprehend the reasoning behind the classification of specific transformations.
  • There is a suggestion that precise definitions are crucial in mathematical discussions to support claims about the nature of transformations.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definitions of even and odd transformations, indicating a lack of consensus on the foundational concepts necessary for the discussion.

Contextual Notes

The discussion lacks clear definitions of "even" and "odd" transformations, which may limit the understanding of the classification of transformations within the D4 group.

LagrangeEuler
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Why ##\rho,\rho^2,\rho^3,\rho^4## are even transformation and ##\rho\sigma,\rho^2\sigma,\rho^3\sigma## are odd transformation. I'm talking about case of ##D_4## group, where ##\rho## is rotation and ##\sigma## is reflection.
 
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Hi LagrangeEuler! :smile:

What is the definition of even (or odd) transformation? :wink:
 
Not sure.
 
LagrangeEuler said:
Not sure.

ok, if you can't give a "mathy" definition, just give an ordinary english explanation (or example), and we'll take it from there :smile:

(go back to your notes or your book, if necessary)
 
tiny-tim's point is, I expect, that you cannot expect to understand any explanation we give as to why a specific transformation is, or is not, even or odd if you do not know what the definition of "even" or "odd" transformation is. And in mathematics definition are "working" definitions- we use the precise words of definitions is proving things. So we would expect to use the precise words of the definitions of "even" and "odd" transformations in proving that certain transformations are even or odd.
 

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