recursively

USAGE SUMMARY

The phrase "recursively" is correct and usable in written English.
It is typically used in contexts related to programming, mathematics, or logic, where a function or process refers to itself in its definition or execution. Example: "The function operates recursively, calling itself until it reaches the base case."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Σ1-) formula of L. Thus the notions of Δ0- and Σ1-set may be regarded as generalizations of the notions of recursive and recursively enumerable set, respectively.

SEP

We have above noted the important fact that in all arithmetical theories F containing Q, a set is strongly representable in F if and only if it is recursive, and a set is recursively enumerable if and only if it is weakly representable.

SEP

A familiar example is the method of diagonalization, as employed in the proof of the undecidability of the classical Halting Problem (from which it follows that the recursive languages are properly included in the recursively enumerable ones).

SEP

There are only countably many recursive functions, so there are only countably many recursively enumerable sets of basic sets.

SEP

A set is recursively enumerable iff it is the range of a (total or partial) recursive function on the natural numbers (Boolos et al. 2003: §8.3).

SEP

Quite independently of the particular formal system chosen, exactly the decidable, or recursive, sets (relations) are strongly representable, and exactly the semi-decidable, or recursively enumerable sets (relations) are weakly representable.

SEP

But the process was slow and laborious.Wizard spellingGoogle applies this principle of recursively learning from the data to many of its services, including the humble spell-check, for which it used a pioneering method that produced perhaps the world's best spell-checker in almost every language.

The Economist

This restricted definition serves as the base-clause for truth-conditional recursion-clauses given at the second stage, at which the truth-values of non-elementary, or molecular, truthbearers are explained recursively in terms of their logical structure and the truth-values of their simpler constituents.

SEP

all continuous t-norms are not recursively axiomatizable (see Montagna 2001 for the final result).

SEP

These clauses can be applied recursively to define transformations of sets of ordered tuples in \(D\) (the extensions of two-place predicates), sets of sets of objects in \(D\) (the extensions of unary first-order quantifiers), and so on.

SEP

Semantics provides a complete account of sentence meaning for the language, [by] recursively specifying the truth conditions of the sentence of the language.

SEP

Expert writing Tips

Best practice

When describing algorithms or data structures, use "recursively" to clearly indicate that the definition or process involves self-reference. This helps readers understand the fundamental approach.

Common error

Avoid using "recursively" when you simply mean "repeatedly" or "iteratively". "Recursively" implies a self-referential process, not just any form of repetition. Using "repeatedly" is better to describe something that merely repeats without a self-reference.

Linguistic Context

The adverb "recursively" modifies verbs or adjectives to describe how an action or characteristic is applied. It signifies that a process or definition involves self-reference, where the function or structure refers back to itself. Ludwig shows examples of the adverd in this context.

Expression frequency: Very common

Frequent in

Science

75%

Encyclopedias

10%

News & Media

10%

Less common in

Formal & Business

2%

Reference

1%

Wiki

2%

Ludwig's WRAP-UP

The adverb "recursively" is used to describe processes or definitions that refer back to themselves. As Ludwig AI confirms, the phrase is grammatically correct and most commonly found in scientific, mathematical, and computational contexts. When using "recursively", ensure that the process truly involves self-reference and not just simple repetition; otherwise, alternatives like ""iteratively"" or "repeatedly" might be more appropriate. The high frequency and consistent usage in authoritative sources underscore its importance in technical communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

by recursion

A more verbose way of expressing the same concept, explicitly mentioning the method of recursion.

in a recursive manner

Similar to 'by recursion' but uses a slightly more formal tone.

self-referentially

Highlights the self-referential nature of the process or definition.

inductively

Commonly used in mathematical contexts to describe definitions built on base cases and inductive steps.

iteratively

Focuses on repetition of a process, but doesn't necessarily imply self-reference in the definition.

through recursive calls

Specifically refers to the act of a function calling itself.

repetitively

Emphasizes the repeated execution of a process, without necessarily implying a structured approach.

successively

Indicates a sequence of steps or operations, but without the self-referential implication.

in a nested fashion

Implies a structure where elements are contained within each other, potentially involving repetition.

algorithmically

Refers to a step-by-step process, which can be recursive or iterative.

FAQs

How is "recursively" used in computer science?

In computer science, "recursively" describes a function that calls itself to solve smaller instances of the same problem, until a base case is reached. This is a fundamental technique in algorithm design.

What's the difference between "recursively" and iteratively?

"Recursively" describes a process that refers to itself in its definition or execution. Iteratively refers to a process that repeats a set of instructions a specific number of times or until a condition is met. While some processes can be implemented both "iteratively" and recursively, the underlying mechanisms are different.

In what contexts is it appropriate to use the term "recursively"?

The term "recursively" is appropriate in contexts involving mathematical definitions, computer algorithms, data structures, and logical arguments where a concept is defined in terms of itself. Outside of these technical domains, the term is rare.

What are some alternatives to using "recursively" in writing?

Depending on the context, you can use terms such as ""iteratively"", "self-referentially", or "inductively" as alternatives to "recursively". The most appropriate term depends on the specific nuance you wish to convey.