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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. At least, this is the convention used in this book and by most category theorists, although it is far from universal in mathematics at large.
Jun 29, 2017 · Lets add some more.... ∼ ∼ is "similar to" but it can also appears in equivalence relations. I suppose similarity is an equivalence relation. ≡ ≡ is "equivalent to" and appears in regularly in modular arithmetic. ≈ ≈ is aproximately. ≅ ≅ is congruence or isomorphism. And of course = = is equality. – Doug M.
Of course, that's a particularly bad idea nowadays, with "!=" the modern shorthand for "not-equals". It's curious --and unfortunate-- that the symbol for emphasis became the symbol for negation. Granted, ASCII isn't the richest glyph set, and coders needed something , but why settle on the symbol that means in prose the exact opposite of what it means in code?
Jan 12, 2018 · 3 Answers. Usually one writes 1 17 ≈ 0.0588. 1 17 ≈ 0.0588. One can write 1 17 = 0.0588 …, 1 17 = 0.0588 …, meaning there are further digits after the 8. 8. I would use the notation “ = 0.0588 … '' “ = 0.0588 … '' only if that last explicit digit is 8 8 and not if it's rounded upward to 8, 8, whereas I would use “ ≈ 0.0588 ...
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 $\div$. Ultimately, the symbol you choose is a matter of personal preference. I personally use $:=$.
An "equality by definition" is a directed mental operation, so it is nonsymmetric to begin with. It's only natural to express such an equality by a nonsymmetric symbol such as :=. Seeing a formula like e =limn→∞(1 + 1 n)n for the first time a naive reader would look for an e on the foregoing pages in the hope that it would then become ...
May 27, 2019 · triple line equals symbol. I keep seeing this symbol ≡ ≡ in Mathematical Analysis -1, Zorich. What does it mean? For example: in page 180 we have, Some other pages it occurs in: 117, 139. This means the function is identically x x, i.e. we have f(x) = x f (x) = x for all x x.
Similarly to how there are many symbols for equivalence relations (or equivalence-like relations) in use, there are many different symbols for orders and partial orders, such as $<,\leq,\prec,\preceq,\subset,\subseteq\dots$, again with some orders exclusively using one symbol over another but symbols being used for multiple things. These symbols more commonly have one end closed with the other end open, suggesting which side is "bigger."
The hat above the equals sign is an estimator. Originaly estimators are used on terms. For example: $$\widehat{\theta}(X)$$ But it has appeared (sometimes) more convenient to use it with an equals sign, especially in statistics. It has transformed a substantive (θ is an estimator for . . .) into a verb. x ≙ . . . then reads as x estimates . . .
Jun 8, 2022 · 3. In Logic, almost all logicians do use "equality" to refer to "=" as in "FOL with [out] equality", as short for "equality symbol". Mathematicians in general prefer to refer to "=" as "equals sign" or "equality sign" or "equality symbol" (with the explicit "symbol"). Yes, "equality" can also refer to a formula of the form " s = t s = t ".
