Abstract - one sided identity question

In summary, the conversation discusses the concept of a left and right identity element, as well as the existence and uniqueness of a one-sided element for *. The conversation also touches on the use of the term "identity element" to refer to both left and right-handed identities, as well as the standard method of proving uniqueness.
  • #1
kathrynag
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0

Homework Statement



I'm trying to find what a a left and right identity element is.
Also, I want to see if a one sided element for * exists, if it is unique.

Homework Equations





The Attempt at a Solution


Ok, I just don't really know what a one sided element is.
I'm using e*s=s*e=s, but is e*s the left identity?
I think my problem with finding uniqueness is getting started and the fact that I don't really understand what a one sided identity element is?
 
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  • #2
e is a left identity, if e * s = s for all s.
It is a right identity if s * e = s for all s.
Usually, when speaking about "an identity element" we mean that it's both left and right-handed (e * s = s * e = e), although it can be shown that it suffices to demand only a left-handed identity (for example) in the group axioms, which will then automatically also be a right-handed identity element.

For the uniqueness: suppose you have two of them, e and e'.
Then e * s = s = e' * s.
 
  • #3
ok, so for uniqueness, I use e*s=e'*s and show that e=e' for uniqueness?
 
  • #4
Yep.
That's actually a very standard way of proving uniqueness (assume that there are two things with the defining property and show that they must be the same).
 
  • #5
Thanks, that makes sense!
 

1. What is an abstract?

An abstract is a brief summary of a research paper, typically about 150-250 words, that provides an overview of the study's purpose, methods, and key findings.

2. What do you mean by "one-sided identity question" in an abstract?

A one-sided identity question in an abstract refers to a research question that is focused on a specific aspect or variable, rather than exploring multiple perspectives. This type of question is often used in quantitative research studies.

3. Why is an abstract important?

An abstract is important because it allows readers to quickly understand the main points and findings of a research paper without having to read the entire document. It also helps researchers determine if the paper is relevant to their own work and interests.

4. How do you write an effective abstract?

To write an effective abstract, you should clearly state the research question or objective, briefly describe the methods and data used, summarize the key results, and provide conclusions or implications of the study. It is also important to use clear and concise language and to be consistent with the tone and style of the rest of the paper.

5. Can an abstract be used as a standalone document?

No, an abstract should always be accompanied by the full research paper. While the abstract provides a summary of the study, it does not include all of the details and nuances of the research, which can only be found in the complete paper.

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