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An impredicative definition is one which defines an object a by a property A which itself involves reference, either direct or indirect, to all the things with that property, and this must, of course, include a itself.
So, by the naive comprehension principle, the condition of being a singer defines an object with exactly that property being a singer and no other properties.
We will sometimes fail to do so and assume that, by abuse of notation, any abstract finite non-empty ordinal defines an object in (Delta ).
For any localizable relative category (langle mathcal {C},W rangle ), a commutative square Open image in new window (2.2 in (mathcal {C}) defines an object (widetilde{c} in mathcal {C}^mathsf{V}), (widetilde{c}(i =c_i), (i=0,1,01), and a map (t:tau (c) rightarrow widetilde{c}).
By (4.22), its fibers are given by begin{aligned} overline{B}(mathcal {C})_{langle [n],x rangle } cong {text {Sec}}_natural ([n]^o,sigma _n^*mathcal {C}), end{aligned}and by definition, any cartesian section in the right-hand side defines an object (langle [n],kappa rangle in Delta ^c_smathcal {C}) that lies in the image of the fully faithful embedding (5.8) of Lemma 5.6.
Plato firstly made the distinction between "is" as a copula in a phrase and the identifying "is"; thus, Aristotle distinguished identity in its numeric meaning as equivalence from an identifier that defines an object as an individual.
Similar(54)
This paper addresses this issue and proposes a component communication framework that defines an object-oriented remote call mechanism which allows transparent communication across hardware/software boundaries.
We define an object model where classes are used to capture design standards and requirements relevant to designed objects.
Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh.
Our gait planning was based on inverse kinematics using the Jacobian of the whole body, where the redundancy was solved by defining an object function for the gecko posture to avoid collisions with the surface.
The first axis defines the orientation of maximum variance and is proportional to the variance magnitude (λ1) defining an object length; secondary and tertiary axis are orthogonal and define in the same way width and height with associated sizes λ2 and λ3, respectively.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com