query: Why does $i \neq 1$?
positive_passages.docid: 3712
positive_passages.text: Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?
negative_passages.docid: 47313
negative_passages.text: What is $i^i$ and $(i^i)^i$
negative_passages.docid: 126633
negative_passages.text: Is a contradiction enough to prove a set equality to $\varnothing$?
negative_passages.docid: 27788
negative_passages.text: Why is the expected value $E(X^2) \neq E(X)^2$?
negative_passages.docid: 93557
negative_passages.text: Intuitively, why does (B → S) ≡ (¬B ∨ S)?
negative_passages.docid: 103536
negative_passages.text: How to prove $|e^{i\theta} - 1| \leq |\theta|$?
negative_passages.docid: 31954
negative_passages.text: Why this proof $0=1$ is wrong?(breakfast joke)
negative_passages.docid: 114736
negative_passages.text: What does 1 with an inequality in the subscript mean?
negative_passages.docid: 31846
negative_passages.text: Does $\neg(x > y)$ imply that $y \geq x$?
negative_passages.docid: 25187
negative_passages.text: Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
negative_passages.docid: 17620
negative_passages.text: Why the principal value of complex number argument is taken within $(-\pi,\pi]?$
negative_passages.docid: 40837
negative_passages.text: Why $e^{i(π/3)} \ne -1$?
negative_passages.docid: 54435
negative_passages.text: What is the value of $1^i$?
negative_passages.docid: 19628
negative_passages.text: What is wrong with this fake proof $e^i = 1$?
negative_passages.docid: 27742
negative_passages.text: What does "${-#*i}" != "$-" mean?
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$