Sentence examples for a foundational point of from inspiring English sources
Since the last step guarantees the consistency of the original theory, from a foundational point of view one is interested in the methods used to prove normalization.
Indeed, from a foundational point of view it does not make much sense to understand the 'proofs' above as proofs in an intuitionistic system which these conditions are supposed to be specifying.
What is important, from a foundational point of view, is that the set-theoretic version of $\mathbb{R}$, together with the usual algebraic operations, satisfies the categorical axioms that the real numbers satisfy, namely those of a complete ordered field.
This has been taken by many to be a vindication of the foundational point of view of mathematical intuitionism.
In the last two decades reflection on predicativity has prospered not only from the foundational point of view but also from the philosophical point of view.
Bernays has written (see Bernays' entry on David Hilbert in Edwards 1967) that this result of Gödel's drew the attention of the Hilbert school to two observations: first, that intuitionistic logic goes beyond finitism, and secondly, that finitist systems may not be the only acceptable ones from the foundational point of view.
This makes APIs among the most foundational points of leverage in modern business ecosystems.
If one takes as foundational a point-of-view that folks are not all the same, we may by choice or necessity rail appropriately against oppression while owning ethically how we have access, if and when we do.
There have also been well-researched and comprehensive proposed guidelines/curriculum for teaching EUS and providing a foundational knowledge of point-of-care ultrasonography.
