I  Is Zero x Infinity Really a Real Number?

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The discussion centers on the mathematical expression 0 times infinity (0·∞), which is considered an indeterminate form rather than a defined real number. Participants argue that multiplying zero by any quantity, including infinity, logically results in zero, as it represents zero iterations of that quantity. However, they also acknowledge that in calculus, the limit of products involving sequences approaching these values can yield various results, including zero, infinity, or other numbers, depending on the context. The conversation highlights the complexities of defining operations involving infinity and emphasizes that traditional arithmetic rules do not apply. Ultimately, the nature of 0·∞ remains a topic of debate, illustrating the intricacies of mathematical definitions and limits.
  • #61
Bipolar Demon said:
Isnt multiplication just glorified addition? so according to my primitive views,=) if so how you can keep adding zero infinitely to get zero IMO.

Sometimes primitive ideas are the most informative.

I could see defining ## x * \infty = x + x+ x + \cdots ## i.e an infinite sequence. Perhaps this has already been said in this thread in a different way.

-Dave K
 
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  • #62
dkotschessaa said:
Sometimes primitive ideas are the most informative.

I could see defining ## x * \infty = x + x+ x + \cdots ## i.e an infinite sequence. Perhaps this has already been said in this thread in a different way.

-Dave K

yes but that series it would (?) seem to diverge to infinity or minus infinity, and converge to zero if x=0. IIRC
 
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  • #63
this man HATES much of set theory and calculus, and real numbers...very interesting debate:





 
  • #64
Bipolar Demon said:
yes but that series it would (?) seem to diverge to infinity or minus infinity, and converge to zero if x=0. IIRC

Well, that's would I would expect it to do!
 
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  • #65
Bipolar Demon said:
this man HATES much of set theory and calculus, and real numbers...very interesting debate:



Yeah, there are some.

I've considered being a finitist if only to be contrary.
 
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