The phrase "arithmetical problem" is correct and usable in written English.
It can be used when referring to a mathematical question or challenge that involves arithmetic operations such as addition, subtraction, multiplication, or division.
Example: "The teacher assigned an arithmetical problem for the students to solve during class."
Alternatives: "mathematical problem" or "numerical problem".
The following example is a typical arithmetical problem that is expressed by the triplet structure model in a combination story: {There are 3 white rabbits (first existence sentence).
The following is a typical arithmetical problem that is expressed by the triplet structure model in a decrease story: {There are 5 apples (first existence sentence).
The problem was twice part of a short story (STORY; e.g., Anna goes for a walk. She walks 4 kilometers per hour. What distance does she cover in 3 hours?), and once the arithmetical problem was formulated (FORMULATION; e.g., What result do you obtain when multiplying 3 by a factor of 4?).
Of course solving arithmetical problems in arithmetic is in some cases practically impossible.
Detlefsen has emphasized that the incompleteness theorems do not preclude that the consistency of parts of higher mathematics that are in practice used for solving arithmetical problems that mathematicians are interested in can be arithmetically established (Detlefsen 1986).
Shapes and sculptures, arithmetical problems, linguistic points moved easily around each other.
When treated with tDCS to their prefrontal cortices, the nervous individuals improved their reaction time on simple arithmetical problems and showed reduced levels of stress.
Some indices incorporate arithmetical problems.
After the training, a "mental abacus" was formed in their brains [ 15, 20], which may be helpful when they performed the arithmetical problems.
When solving arithmetical problems, participants with high maths anxiety have higher error rates, they have problems with rejecting incorrect solutions (even when these are highly implausible), and these effects are especially prominent in the case of more complex problems which require a carry operation (e.g., [ 15, 16]).
If the only ways of proving the consistency of arithmetic make essential use of notions which arguably belong to higher-order mathematics, then the consistency of arithmetic, even though it can be expressed in the language of Peano Arithmetic, is a non-arithmetical problem.
