Sentence examples for concepts of standard from inspiring English sources

One main achievement of early mathematical logic was precisely to show how to characterize notions of derivability and validity in terms of concepts of standard mathematics.

Another of the reasons is that the fact that the grammar and meaning of the artificial formulae is so well delimited has permitted the development of proposed characterizations of logical truth that use only concepts of standard mathematics.

This is especially true for the notions of set and collection in general, for the basic syntactical and semantical concepts of standard classical logic (logical languages of a given order, the notion of satisfiability, definability).

And even among those who accept it, there is little if any agreement about what generic criteria determine the form of an arbitrary sentence.[1] A remarkable fact about logical truth is that many have thought it plausible that the set of logical truths of certain rich formalized languages is characterizable in terms of concepts of standard mathematics.

Tarski (1936a, 1936b) was the first to indicate in a fully explicit way how the version of universal validity used by the mathematicians could itself be given a characterization in terms of concepts of standard mathematics, in the case of Fregean formalized languages with an algorithmic grammar.

So the derivable formulae can be seen as (or codified by) the numbers obtainable from the axiom numbers after some finite series of applications of the inference operations, and thus their set is again characterizable in terms of concepts of standard mathematics (again arithmetic suffices).

But "this concept of standard precautions has not yet been deeply rooted in many trainees," Dr. Schaffner said.

The railroad industry literally helped invent the concept of standard time, and time zones were established in the United States in the 1880s, 35 years before they were written into law.

Obviously, if we choose Definition 1.1 recaptures the concept of standard convex functions on.

The concept of standard metric spaces is a fundamental tool in topology, functional analysis and nonlinear analysis.

Järvilehto — who also founded and directed a think tank called the Helsinki Academy of Philosophy — eschews gamification and the concept of standard learning ushered through branded content.