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Feb 23, 2017 · This is what confused me about the definition, for I have sometimes thought of $\neq$ as meaning that they are never the same. As a bonus question; would the negation of ($\ref {3}$) have any meaning?
3 I have seen similar questions (perhaps too similar, I´m sorry if so) but none of them do too much of a good job on defining what an expression such as $$\sum_ {i\neq j}^n (x_iy_j)$$ means exactly. What set of number...
Jun 14, 2023 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead,...
Mar 1, 2015 · Closed last year. In the definitions of a field, we have $ 1 \neq 0$. I know that in regular multiplication $0 \times 1=0$ but for reciprocal we don't have inverse of $0$. But all the spaces and differen...
You have $AB\neq 0$ but $BA=0$. Rings in which $ab=0$ implies $ba=0$ are called reversible rings. That is a particularly strong condition, and is pretty interesting to study. I highly recommend Greg Marks' paper: Reve...
Nov 21, 2024 · Let $G$ be a group and $H$ be a subgroup of $G$ with finite order such that for all $F$, which is a subgroup in $G$ it holds: $F\neq H \Rightarrow |F|\neq |H|$.
Oct 14, 2023 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead,...
May 18, 2024 · Then $ \mathcal {R}^ {\neq} $ is transitive and a strict partial ordering on $ X $. $\blacksquare$ Theorem. Inclusion, $ \subset $, is a partial ordering on every power set $ \wp (X) $. Proof. We need t...
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