The arithmetization of analysis clarified which results could be derived purely from arithmetic, reshaping the foundations of mathematics.

The proof compared several arithmetizations to show that the encoding was robust across different representations.

When solving the problem, she mistakenly used an arithmetic operator that changed the sign of the result.

Graduate students in logic often study arithmetical sets to understand the limits of computability.

The arithmetical set of numbers defined by a first-order Peano arithmetic formula is not always decidable.

When deciding policy, she relied on moral arithmetic to weigh the benefits and harms of each option.

Researchers compared several arithmetic functions to determine which best modeled the data.

The mathematician sketched an arithmetic spiral on the chalkboard to illustrate linear radial growth.

When comparing multiple data sets, the arithmetic means often reveal trends that medians do not capture.

To determine the descriptive power of different fragments, researchers examine the arithmetical hierarchy, which classifies the complexity of first-order formulas and the sets they define by counting alternations between blocks of unbounded existential and universal quantifiers.