The phrase "arithmetic based on the" is correct and usable in written English.
It can be used when discussing mathematical concepts or methods that rely on a specific foundation or principle.
Example: "The new curriculum emphasizes arithmetic based on the principles of number theory to enhance students' understanding of mathematics."
Alternatives: "mathematics grounded in the" or "calculations derived from the".
This applies, in particular, to the aforementioned theories Ta and Tb of arithmetic (based on the language of N), the natural models of which are countable, as well as to theories dealing with real numbers and arbitrary sets, the natural models of which are uncountable; both kinds of theory have both countable and uncountable models.
Meyer has produced a variation of Peano arithmetic based on the logic R. Meyer gave a finitary proof that his relevant arithmetic does not have 0 = 1 as a theorem.
We focus on inequalities that employ arithmetic functions based on the divisors of positive integers.
In the proposed structure, weights are stored in the digital registers while the arithmetic is based on the CVNS.
It is verified that the proposed variable rate coder with the adaptive arithmetic coding based on the time-frequency context produces the same audio quality as the original G.719 coder while achieving a high coding gain.
The mean SMBGs were calculated with an arithmetic mean based on the three 7-point BG profiles.
When multiple informants were used (e.g., rates of anxiety were reported separately for the child, parent, and/or teacher), a weighted arithmetic average (based on the number of each informant) of these rates was entered into the meta-analyses.
The range for each label was defined as: If 1 ≤ m < 1.5 → FORTA Class A If 1.5 ≤ m < 2.5 → FORTA Class B If 2.5 ≤ m < 3.5 → FORTA Class C If m ≥ 3.5 → FORTA Class AD where m = arithmetic mean based on the raters' grades 1 4.
The dendrogram was generated with the UPGMA (unweighted pair group method with arithmetic mean) method based on the internal fragments of 7 housekeeping genes of the 17 strains.
Finally, the constraints to form arithmetic word problems based on the task model are discussed and followed by a number of case examples.
