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Nov 5, 2017 · Making a machine understand "abuses of notation", sometimes, makes the job easier and more robust for humans (as long as the semantics stays clear), even if it means that the machine (be it real hardware, or be it virtual, as an interpreter program) will work harder to get the job done.
Abuse of notation should be contrasted with misuse of notation, which does not have the presentational benefits of the former and should be avoided (such as the misuse of constants of integration [1]). A related concept is abuse of language or abuse of terminology, where a term — rather than a notation — is misused. Abuse of language is an ...
Dec 24, 2012 · Abuse of notation is tolerated when the alternative is worse! In some cases, abuse of notation isn't really abuse at all, but simply a lack of fleshing things out. For example, I'm sure many would consider. arctan(+ ∞) = π / 2. an abuse of notation that is meant as shorthand for. lim x → + ∞arctan(x) = π / 2.
Indeed. OP, please do not say "abusive maths" to mean "abuse of notation". Saying “abusive math” to mean “abuse of notation” is just an abuse of language. yup, and to illustrate the point, "abuse of language" is NOT the same as "abusive language". it sounds absolutely hilarious since all math is abusive.
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I've never quite understood why mathematical notation has a place in most machine learning papers. Mathematical notation is still quite good for proving two equations are equivalent or a statement is true (arguably the same thing). However, most machine learning papers deal with dynamic processes that rely on very fundamental mathematics.
Nov 18, 2014 · Also: $\sin^{-1} x$ is definitely an abuse of notation. It is not the inverse function, but refers to the inverse of a specific restriction of $\sin x$ to a domain on which it's injective. Note that $\cos^{-1}$ and $\tan^{-1}$ are also used, and their restrictions are different. This notation can only be defined in an extremely kludgy way.
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Oct 16, 2021 · Abuse of notation is a technique of using a system of symbology in a way different from that for which it was originally defined. Such abuse may make a train of thought more streamlined, as it is often possible to save considerable redefinition of one's terms. However, such abuse is frequently considered to be incorrect, improper and (in the ...
