Solving Asymptote Ambiguity: Find Attachment

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    Asymptote
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Discussion Overview

The discussion revolves around the concept of asymptotes in mathematics, particularly focusing on the definitions and implications of domain restrictions. Participants explore informal definitions, proofs, and the relationship between asymptotes and domain restrictions, with references to shared documents for clarification.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant requests feedback on an attachment related to asymptotes, indicating potential ambiguity.
  • Another participant expresses reluctance to open attachments from strangers, suggesting the original poster should share the content directly in the thread.
  • A participant questions the relevance of domain restrictions to asymptotes, indicating confusion and sharing a PDF document for reference.
  • One participant acknowledges that their informal definition of asymptotes may be confusing and expresses a desire to provide a clearer proof in the future.
  • Another participant critiques the informal proof, noting that while it is acceptable, it lacks the rigor typically expected in mathematical proofs and highlights potential gaps in the definition of asymptotes related to domain restrictions.
  • A later reply expresses gratitude for the feedback received, indicating a willingness to engage further.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the definitions and implications of asymptotes, with multiple competing views and some confusion expressed regarding the relationship between asymptotes and domain restrictions.

Contextual Notes

There are limitations in the definitions provided, particularly regarding the informal nature of the proofs and the assumptions about domain restrictions and asymptotes that remain unresolved.

Didd
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Hello

Look for the attachment and if you found any ambiguity, please reply.
 

Attachments

Last edited:
Mathematics news on Phys.org
You're crazy (or malicious) if you think I'm going to open the Word doc of a complete stranger.

Don't be lazy - post it.
 
What does domain restriction have to do with asymptotes ? :confused:

-gaz

btw i exported to pdf because i have no life and should be studying. :P aah the wonders of procrastination. It's amazing how clean your room gets when you have exams :rolleyes:

http://abyss.zapto.org/temp/Asymptote.pdf
 
Last edited by a moderator:
It is informal defination. Truly, it confuses a lot if you are not patient enough to grasp the idea.

At this time, I was unable to delete the message. On other time, I might resend it with clear and formal way of prooving it. What I prsented there is , "Informal way of prooving". I appolgise for that. I on my way, was trying to make my idea very easy but the outcome is unattractive.
 
What you wrote looks OK to me but it's definitely not what I'm used to seeing in a proof (you're right it was very "informal") and I have a few holes to fill in (pun intended). You say that asymptotes are *the* restriction of the domain of the domain/range of a function. You also say that if the numerator of f(x) = 0 then f(x) has no asymptotes and, by your definition, no restrictions in the domain. What if the denominator is a polynomial of x of degree greater than 0? For example, f(x) = 0/(x-1) is not defined at x = 1 and therefore has a domain restriction (but you're right it isn't an asymptote) so I think you may want to refine your alternate definition of an asymptote a little. I like most of the rest of it though.
 
Vsage,

I am glad about your responce.

Thank you
 

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