The phrase "arithmetical problems" is correct and usable in written English.
It can be used when referring to mathematical questions or exercises that involve arithmetic operations such as addition, subtraction, multiplication, and division.
Example: "The teacher assigned several arithmetical problems for the students to solve during class."
Alternatives: "mathematical problems" or "numerical problems".
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).
Some indices incorporate arithmetical problems.
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.
Finally these results are applied again to the starting arithmetical problems.
It is true that abandoning plans to raise national insurance contributions (NICs) for some self-employed workers means the numbers no longer add up, so Philip Hammond has an arithmetical problem on his hands, which will become a revenue-raising 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?).
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.
