notation - What does := mean? - Mathematics Stack Exchange Other symbols I have seen used for "is defined to be equal to" are three horizontal lines instead of two, and $=$ with either a triangle or "def" written directly above it I have seen variants of these used by people who predate widespread knowledge of computer programming It would be interesting to know the earliest uses of a special symbol for this (and what symbols were chosen) An
notation - what does ≼ or ≺ mean? - Mathematics Stack Exchange I was reading a paper about well-orderings and this came up: Suppose (E, ≤) and (F, ≼) are isomorphic well-orderings Then there exists a unique isomorphism for (E, ≤) to (F, ≼) I've been scouri
What is the difference between ⊢ and ⊨? - Mathematics Stack Exchange I learned that $\models$ stands for semantic entailment, while $\vdash$ stands for provability in a certain proof system More concretely: Given a set of formulas $\Gamma$ and a formula $\varphi$ in some logic (e g , first-order logic), $\Gamma \models \varphi$ means that every model of $\Gamma$ is also a model of $\varphi$ On the other hand, fix a proof system (e g , sequent calculus) for
What is the meaning of ⊊? - Mathematics Stack Exchange I have encountered this when referencing subsets and vector subspaces For example, T ⊊ span(S) should mean that T is smaller than span(S)--at least from what I've gathered Is ⊊ a sort of ≤ or lt
Whats the difference between theorem, lemma and corollary? Can anybody explain me what is the basic difference between theorem, lemma and corollary? We have been using it for a long time but I never paid any attention I am just curious to know
algorithms - Meaning of “arg min” - Mathematics Stack Exchange Please provide additional context, which ideally explains why the question is relevant to you and our community Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc
inequality - What does lt; gt; mean? - Mathematics Stack Exchange What do the less-than and greater-than symbols right next to each other mean? Does it mean either less than or greater than? In other words, not equal? I am trying to understand a book that says th