Why Is 0 Divided by 0 Undefined?

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Homework Help Overview

The discussion revolves around the concept of dividing zero by zero (0/0) and why it is considered undefined in mathematics. Participants explore various interpretations and implications of this expression, touching on foundational concepts in arithmetic and limits.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Some participants attempt to define 0/0 in various ways, questioning the implications of such definitions. Others explore the consequences of assuming 0/0 is defined, leading to contradictions. There are discussions about the nature of undefined versus undetermined forms, and the relevance of limits in calculus.

Discussion Status

The conversation is ongoing, with multiple interpretations being explored. Participants have raised questions about the definitions and implications of 0/0, and some have offered insights into potential proofs or reasoning approaches. There is no explicit consensus, but several productive lines of inquiry have emerged.

Contextual Notes

Participants note that the question may be poorly worded and that definitions can vary depending on context. There is mention of specific mathematical functions, such as the sinc function, which complicate the discussion around 0/0. Additionally, the distinction between undefined and undetermined forms is highlighted.

  • #31
(0*n)/0 = 0*(n/0)

This step is incorrect. With IBM's implementation (a*b)/c is not necessarily a*(b/c) - in fact this fails not only when c=0.

It is necessary to live with the consequences of what has been defined. But what has been defined in any given circumstance is not generally a matter for proof. IBM give you some very good manuals. These tell you what is defined and what the definition are.
 
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  • #32
That's all fine and good (and of some interest, though it's a strictly decreasing function over time), but with the OP in mind -
WHAT does this have to do with the QUESTION! Is this kid in an IBM class? Is he even a kid (or male)? ;)
I imagine a h.s. or undergrad student thinking "what the $%^ are they talking about?!". Can we help this guy get some closure, or just regurgitate an endless stream of advanced topics? I personally don't mind talking about this stuff, but we should do that elsewhere.
 
  • #33
I would imagine that OP had got all he wanted to from the thread long before you reopened it.
 
  • #34
Martin Rattigan said:
I would imagine that OP had got all he wanted to from the thread long before you reopened it.

Let's hope so! Funny word choice, though. "reopened" implies closure, which wasn't apparent (at least to me) in the 1-hour gap between my first post and the post immediately preceding that...
 
  • #35
Thank you all for your input. This question actually appears in Calculus by Varberg, Purcell, and Rigdon and I encountered while I was going through the pages to refresh my calculus.
 

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