query: Can we imagine some strange "unit" $ S $ such that $ S \times 0 = 1 $?
positive_passages.docid: 22890
positive_passages.text: Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
negative_passages.docid: 5022
negative_passages.text: Can a set containing $0$ be purely imaginary?
negative_passages.docid: 149605
negative_passages.text: Homeomorphism from $[0,1]\times[0,1]$ to $\overline{D}(0,1)$?
negative_passages.docid: 14150
negative_passages.text: Zero to the zero power – is $0^0=1$?
negative_passages.docid: 143586
negative_passages.text: Is $[0,1]$ a union of family of disjoint closed intervals?
negative_passages.docid: 106884
negative_passages.text: Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?
negative_passages.docid: 4156
negative_passages.text: What is $\Bbb R^{\times}$? [unit group, ring to "times" power]
negative_passages.docid: 53361
negative_passages.text: If a measure only assumes values 0 or 1, is it a Dirac's delta?
negative_passages.docid: 10760
negative_passages.text: Why is the product of all units of a finite field equal to $-1$?
negative_passages.docid: 61673
negative_passages.text: Could I define 0^0 to be 1?
negative_passages.docid: 83713
negative_passages.text: If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
negative_passages.docid: 148993
negative_passages.text: Can the initial time be non-zero?
negative_passages.docid: 109219
negative_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 27567
negative_passages.text: What is zero times infinity?
negative_passages.docid: 50133
negative_passages.text: The sum of odd powered real numbers equals zero implies the numbers are inverses
negative_passages.docid: 122916
negative_passages.text: Does $[0.9999....]=1$?
negative_passages.docid: 69228
negative_passages.text: Factorial of 0 - a convenience?