The phrase "completeness without" is grammatically correct and is often used in written English.
It is typically used to describe something that is lacking or missing in completeness or entirety. Example: "The report was praised for its thoroughness, but the analysts discovered a flaw in the completeness without further analysis."
Without aiming completeness, and without going into any details, we refer to Stacy and Mihram (1965), Harter (1967), Rahman and Gokhale (1996), Varanasi and Aazhang (1989), Do and Vetterli (1988), Mineo and Ruggieri (2005), González-Farías et al. (2009), Saatci and Akan (2010).
A German officer attached to the Third Army described the defeat as "a disaster which for rapidity and completeness is without parallel in military history".
Mathematical fictionalists should first be able to prove the completeness result without assuming set theory.
In this theorem, we consider only a completeness hypothesis without assuming the continuity of the nonself-mapping.
In this theorem, we consider only a completeness hypothesis without assuming the continuity of the non-self mapping and the approximate compactness of the subspace.
In this theorem, we consider only a completeness hypothesis without assuming the continuity of the non-self-mapping and the approximatively compactness of subspace.
The problem with this move is that, even if mathematical fictionalists formulate the statement of the completeness theorem without referring to mathematical entities, the proof of this theorem assumes set theory (see, for instance, Boolos and Jeffrey 1989, pp. 131 140).
In this section, we present sharpened forms of Theorems 1-4, which are new results on their own and are proved without completeness (of the metric space), without continuity (of the underlying mapping) and without the ICU property/DCL property/MCB property (of an ordered metric space).
(f) Let us finally mention that properties of Definitions 3.1-3.3 3.1-3.3orems 4.1 and 4.2 concerning 'righTheoremsomitted in our presentation; we may provide them by constructing appropriate examples (without assuming that T is continuous, without completeness of spaces in a usual sense and without separability of spaces) and applying analogous technique as above.
The method uses only three input parameters and allows for efficient compensation between completeness and correctness, without significantly affecting the F1-score.
