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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.
May 27, 2019 · Having said that, ≡ ≡ is neither necessary nor sufficient for an identity. It's unnecessary because, for example, I've never seen anyone bother writing sin 2x ≡ 2 sin x cos x sin 2 x ≡ 2 sin x cos x. In theory we should for clarity; but clarity is more important in some places than others. Zorich probably uses ≡ ≡ because you need ...
Mar 18, 2011 · 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?
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 $:=$.
Jan 12, 2018 · Answer from comments: Usually one writes $\dfrac 1 {17} \approx 0.0588.$. One can write $\dfrac 1 {17} = 0.0588\ldots,$ meaning there are further digits after the $8.$ I would use the notation $\text {“ } =0.0588\ldots \text { ''}$ only if that last explicit digit is $8$ and not if it's rounded upward to $8,$ whereas I would use $\text ...
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 e = lim n → ∞ (1 + 1 n) n for the first time a naive reader would look for an e e on the foregoing pages in the ...
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 . . .
Is there a symbol for potential equality? Essentially I'd like to condense: (a = b) ∨ (a ≠ b) (a = b) ∨ (a ≠ b) so that I can express the phrase "a may or may not be equal to b". Apologies if my syntax is not entirely correct; I come from a computer science background. notation. Share.
Jul 28, 2010 · Any mathematical notation is ok as long as it is common knowledge in your community. For instance, I believe I fully understand the meaning of the $\approx$ symbol. However, I haven't ever seen the second symbol you provided. To be on the sure side you should provide a definition of any relation symbol you don't consider to be common knowledge.
