In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B...

Jul 28, 2021 · 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 …

Dec 22, 2020 · 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 …

Mar 5, 2011 · 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 …

I have read that an infinitesimal is very small, it is unthinkably small but I am not quite comfortable with with its applications. My first question is that is an infinitesimal a stationary value?...

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 …

Jun 25, 2014 · I have started seeing the "∈" symbol in math. What exactly does it mean? I have tried googling it but google takes the symbol out of the search.

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...

May 6, 2015 · Maybe instead of handling your example, because the context is not always relevant, let's look at possible groupings of the symbols. Equality $=$ is usually used for equality. $\equiv$ is …

Jul 22, 2010 · In summary: The interplay of meaning and axiomatic machine mathematics, captured by the difference between $\models$ and $\vdash$, is a subtle and interesting thing.