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For p, q ∈ E ∞, p and q are tail equivalent (written p ∼ q ) in case there exist integers m, n for which p > m = q > n (i.e., in case p and q eventually become the same infinite path).
The set of all words accepted by M is called the language accepted by M. For every machine M, the machine ({mathrm {Sym}}(M)) is made from M by adding the inverses of all commands of M. Two configurations w, (w') are called equivalent, written (wequiv _M w'), if there exists a computation of ({mathrm {Sym}}(M)) connecting these configurations.
Two functions on the naturals (gamma _1) and (gamma _2) are called equivalent (written (gamma _1sim gamma _2)) if there is a constant (Cin mathbb N ) such that ( gamma _1(n) le Cgamma _2(Cn),)(gamma _2(n) le Cgamma _1(Cn)) for all (nge 1).
Any non-zero element x ∈ P is called a ray of P. Two rays r and r' are equivalent, written r ≅ r', if r = λr', for some λ > 0. A ray r in P is extreme if there do not exist rays r', r"∈ P, r' ≇ r" such that r = r' + r".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com