arithmetical

USAGE SUMMARY

'arithmetical' is a correct and commonly used word in written English.
It is an adjective that describes something related to or involving arithmetic, which is the branch of mathematics dealing with numbers and basic operations like addition, subtraction, multiplication, and division. You can use 'arithmetical' in a sentence to describe a problem or equation that involves numbers and basic operations: - The students were given a set of arithmetical problems to solve for their math homework. - The arithmetical skills of the child were impressive for their age. - The calculator has both scientific and arithmetical functions. - The game requires players to use their arithmetical abilities to solve puzzles and progress to the next level. - The arithmetical average of the test scores was 85%.

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Rules of inference also get expressed in the arithmetized form: For example, there is an arithmetical formula M x, y, z) which is true exactly when one has an application of a standard rule of inference "Modus Ponens" at hand; i.e., for some formulas A and B, x = ⌈A⌉, y = ⌈A → B⌉ and z = ⌈B⌉.

SEP

Solovay's completeness theorem provides an alternative way to construct many arithmetical sentences that are not provable in Peano Arithmetic.

SEP

This shows that V² 0, S, +, ×) cannot be arithmetical (i.e., cannot be first-order definable in arithmetic), lest truth in arithmetic be definable, in violation of Tarski's theorem.

SEP

(2) Whenever an interpretation of a result of symbolical algebra made sense in the setting of arithmetical algebra, the result would give a correct result in arithmetic.

SEP

Most of them are unwilling to admit that the preference of arithmetical systems in which the arithmetical sentence expressing the consistency of Peano Arithmetic are derivable over those in which its negation is derivable, for instance, can ultimately be explained in purely pragmatical terms.

SEP

Scoring 28% from nowhere is certainly an arithmetical achievement for the rightwing insurgents, and – by changing the subject from Europe to immigration – they demonstrated that Mr Cameron's referendum initiative is not going to see them off.

The Guardian - Opinion

Ms Livni, who came from behind to pip Mr Netanyahu at the post, is still fighting hard to keep him out of the prime minister's seat, despite the arithmetical handicap dealt by the results.

The Economist

This process might have been a good idea helping to rebut the charge that the party had few policies if it hadn't been for the backtracking and arithmetical embarrassments it has entailed.

The Economist

But it is striking that the main arithmetical conundrum Mr Cameron needs to explain is where he will find the money to fund his various spending pledges, rather than which public services he will slash to finance putative tax cuts.

The Economist

Hitherto, the government's instinct was to withdraw into arithmetical obfuscation.

The Economist

Yet that may be ignoring a simple arithmetical fact: at present over 90% of the world's water is delivered by publicly owned bodies, so there is no doubt that the Johannesburg goals will have to be met substantially by the public sector.Private suppliers have in fact long played a role in water.

The Economist

Expert writing Tips

Best practice

When using "arithmetical", ensure the context clearly involves calculations and basic numerical operations. It's most appropriate when distinguishing from more advanced mathematical concepts.

Common error

Avoid using "arithmetical" when the context requires a term encompassing more than just basic numerical operations. Terms like "mathematical" or "computational" might be more appropriate for advanced calculations or non-arithmetic mathematical concepts.

Linguistic Context

The adjective "arithmetical" functions primarily as a pre-modifier, describing nouns related to arithmetic. As Ludwig AI indicates, this includes concepts, methods, or problems involving numerical calculations and basic mathematical operations.

Expression frequency: Very common

Frequent in

Science

46%

News & Media

39%

Encyclopedias

9%

Less common in

Formal & Business

3%

Reference

0%

Wiki

0%

Ludwig's WRAP-UP

The adjective "arithmetical" is a grammatically sound and frequently used term, especially within scientific and news contexts. As Ludwig AI shows, it denotes something relating to arithmetic, specifically basic numerical calculations. When writing, ensure the term accurately reflects the context of basic numerical operations, differentiating it from broader mathematical or computational concepts. Ludwig's examples show the variety of ways "arithmetical" is used across academic and media publications, confirming its widespread acceptance and correct usage.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

arithmetic

The noun form of the adjective, referring to the branch of mathematics dealing with numbers and their operations.

relating to arithmetic

A more descriptive way of saying "arithmetical", clarifying the connection to arithmetic.

numerical

Emphasizes the use of numbers in general, rather than the specific operations of arithmetic.

mathematical

Broader term encompassing all aspects of mathematics, including arithmetic.

number-based

Similar to numerical, but specifically emphasizes the reliance on numbers.

calculation-based

Focuses on the process of calculating, implying arithmetic is involved.

computation-related

Highlights the computational aspect, suggesting the use of arithmetic in computations.

involving calculation

Highlights the involvement of calculations or computations, which may or may not be exclusively arithmetic.

quantitative

Focuses on the quantity or amount, suggesting the use of numbers and arithmetic in analysis.

algebraic

Related to algebra, a broader field of mathematics that often builds upon arithmetic.

FAQs

How is "arithmetical" used in a sentence?

You can use "arithmetical" to describe something related to arithmetic. For example, "The students were given a set of arithmetical problems to solve."

What's the difference between "arithmetical" and "mathematical"?

"Arithmetical" specifically relates to arithmetic (basic numerical operations), while "mathematical" is a broader term encompassing all aspects of mathematics.

When should I use "arithmetical" instead of "numerical"?

Use "arithmetical" when referring to calculations and operations involving numbers. Use "numerical" when referring to data represented by numbers.

Is "arithmetical" interchangeable with "calculation-based"?

While related, "arithmetical" refers specifically to operations like addition, subtraction, multiplication, and division. "Calculation-based" is more general, encompassing any process involving calculations, which may or may not be exclusively arithmetic.