There, you'll find distinctions in the way the equality symbol is used in logics: FOL (First Order Logic) with identity (where = is a primitive logic symbol), and this is what your author intends …

2015年5月6日 · Equality $=$ is usually used for equality. $\equiv$ is occasionally used for "identically equal to," which is in a sense stronger than equality, by denoting that the thing on …

There's equality at the meta-level (where we're talking about structures, interpretations, formulas and so forth), and the equality symbol that can appear in a formula. Unfortunately it is common …

The symbol ≅ is used for isomorphism of objects of a category, and in particular for isomorphism of categories (which are objects of CAT). The symbol ≃ is used for equivalence of categories. …

The most common one however is $ := $. The symbol $\equiv$ is usually used to denote a logical equivalence. The symbol $\stackrel{\mathrm{def}}=$ should just be exiled along with $\div$. …

2011年3月18日 · 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 …

2023年6月25日 · Let's talk about the FOL with equality as it seems the one most logic books talk about. For FOL without equality, it seems easier to understand the meaning of "=" which is …

Is there a symbol for potential equality? Essentially I'd like to condense: $$ (a = b) \lor (a \ne b) $$ so that I can express the phrase "a may or may not be equal to b". Apologies if my syntax is …

2017年6月29日 · I suppose similarity is an equivalence relation. $\equiv$ is "equivalent to" and appears in regularly in modular arithmetic. $\approx$ is aproximately. $\cong$ is congruence …

and "What is the relation between these two expressions?" and I was hoping for an answer to the latter. In any case their answer might be the same "There is a solution ⇔ These expressions …