The discussion centers on the mathematical expression of zero multiplied by infinity (0 × ∞) and its classification as an indeterminate form. Participants argue that while zero times any finite number is definitively zero, the multiplication of zero by infinity leads to undefined results depending on the context, particularly in calculus and limits. The conversation highlights the necessity of defining multiplication in the context of real numbers and the implications of treating infinity as a quantity. Ultimately, the consensus is that 0 × ∞ cannot be simplistically defined as zero without considering the broader mathematical framework.
PREREQUISITESMathematicians, students of calculus, educators teaching advanced mathematics, and anyone interested in the philosophical implications of mathematical definitions and operations.
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.
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
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
Bipolar Demon said:this man HATES much of set theory and calculus, and real numbers...very interesting debate: