Why Is 0 Divided by 0 Undefined?

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SUMMARY

The discussion centers on the mathematical concept of dividing zero by zero (0/0), which is universally recognized as undefined. Participants argue that defining 0/0 leads to contradictions, as it could be assigned any value, thereby violating the uniqueness of division. The conversation also touches on the distinction between "undefined" and "indeterminate," with references to the sinc function and limits in calculus. Ultimately, the consensus is that 0/0 cannot be consistently defined without leading to logical inconsistencies.

PREREQUISITES
  • Understanding of basic arithmetic operations and their definitions.
  • Familiarity with limits and continuity in calculus.
  • Knowledge of mathematical logic and proof techniques.
  • Awareness of the concepts of "undefined" versus "indeterminate" in mathematics.
NEXT STEPS
  • Study the concept of limits in calculus, particularly L'Hôpital's Rule.
  • Explore the definitions of indeterminate forms and their implications in calculus.
  • Research the differences between undefined and indeterminate expressions in mathematics.
  • Examine the sinc function and its behavior at x = 0 for better understanding of continuity.
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Students in mathematics, educators teaching calculus, and anyone interested in the foundational concepts of arithmetic and limits.

  • #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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