Sentence examples for arithmetic definition from inspiring English sources

While accepting the arithmetic definition of the continuum, he questions the fact that (as with Dedekind and Cantor's formulations) the (irrational) numbers so produced are mere symbols, detached from their origins in intuition.

In this Part, we give information on Nichols algebras ({mathcal {B}}_{mathfrak {q}}) for matrices (mathfrak {q}) satisfying (2.1) such that (mathfrak {q}) is arithmetic, see Definition 2.12, and has a connected Dynkin diagram.

(When added to first-order arithmetic, these definitions render all \ \Pi^{1}_{2}\) sets of natural numbers definable).

This is because the method textbook (Reys et al. 2009) only briefly presented the definition, arithmetic examples, and the algebraic formula for the AP of multiplication, which targeted only the CCK but not SCK.

Furthermore CADNA contains the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments.

The core of the language remains the same (variable definition, conditions, arithmetic and boolean expressions, etc).

This seemed to require a truth definition for arithmetic, which in turn led to paradoxes, such as the Liar paradox ("This sentence is false") and Berry's paradox ("The least number not defined by an expression consisting of just fourteen English words").

As explained in "Types of constraints based on task model of problem posing" section, these constraints are derived from the task model of problem posing, which is built according to the definition of arithmetic word problems in the Triplet Structure Model.

For this definition the arithmetic mean of the 10 concentrations that had been calculated and assigned as described above was used as the mean exposure concentration of every individual bather.

But few of Frege's definitions of arithmetic concepts are nearly so simple (see Gottlob Frege, §2.5).

Frege and neo-Fregeans following him believe that arithmetic is logic (plus definitions) and that numbers are objects whose existence is implied by arithmetic.