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(ii) Statement (ii) follows immediately from Statement (i).
(ii) Statement (i) implies that f ( s q k + ω [ k ] q ) = f ( s ) for every s ∈ I and k = 0, 1, … .
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Part I: Terms Part II: Statements: Part III: Argumentation The reader can easily see that this treatment of "all of logic" corresponds to a large extent to what is found in many 'modern' logic books prior to the treatment of predicate logic.
Vatican II's statement on the subject could not be more clear-cut: "The Vatican Council professes its belief that it is upon the human conscience that these obligations [to seek the truth] fall and exert their binding force. . . .
To commemorate Roosevelt's third term (in which he helped win World War II), his statement "I hate war" is given pride of place and is inscribed on a pile of shattered stone.
The Coupe de Ville, powered by the company's first overhead valve V-8, represented a revolutionary new post-World War II styling statement from G.M. It cost a reported $30,000 – nearly $300,000 today – and took more than two months to build.
(ii) The statement on sponsorship was false.
The Four Freedoms' theme was later incorporated into the Allies' World War II policy statement, the Atlantic Charter, and became part of the charter of the United Nations.
Statement (ii) follows immediately from Statement (i).
In this section I will limit myself to four issues (i) the function of realisation; (ii) realisation statements; (iii) selection expression; and (iv) the trinocular perspective.
For this, we present the following results: (i) A proof of the necessary Lloyd-Max conditions for optimality of a graph quantizer, (ii) consistency statements for optimal graph quantizer design, and (iii) an accelerated version of competitive learning graph quantization.
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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