Sentence examples for exactly the same properties from inspiring English sources
There is no single multilinear extension of the SVD, with exactly the same properties as the SVD.
Nodes within a group cannot be differentiated because they all share exactly the same properties of the group.
Leibniz's Law says that if x = y (i.e. x and y are identical one and the same entity) then x and y have exactly the same properties.
This is often referred to as 'Leibniz's Law' and is typically understood to mean that no two objects have exactly the same properties.
Instead of saying, for instance, that a and b have exactly the same properties, one says that exactly the same formulas are true of a and b.
Actually, Leibniz called his definition "the identity of indiscernibles" and gave it in the form of a biconditional: x and y are the same if x and y have exactly the same properties.
To say that psychological properties supervene on physical properties, for example, is to say that, necessarily, everything that has any psychological properties also has physical properties and any two things that have exactly the same physical properties will have exactly the same psychological properties.
Parsons's individuation principle for objects is the following: "(1) No two objects (real or unreal) have exactly the same nuclear properties; and (2) For any set of nuclear properties, some object has all the properties in that set and no other nuclear properties" ([Parsons 1980, 19]).
Since Oscar and Twin Oscar have exactly the same intrinsic properties, yet refer to different substances when they use their 'water'-words, their intrinsic properties cannot suffice to determine what they refer to.
