by corollary

USAGE SUMMARY

"by corollary" is a correct and usable phrase in written English.
You can use it to draw a conclusion based on a previous statement or result; for example, "We found that the optimum temperature for the experiment is 24 degrees Celsius. By corollary, temperatures beyond 24 degrees Celsius are not ideal for this particular experiment."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

By Corollary 3.4, we can get that (3.22).

Journal of Inequalities and Applications

By corollary, unused NH3 capacity exists downstream of the SCR zone.

Applied Catalysis B: Environmental

By Corollary 4.4, admits MP.

Boundary Value Problems

This is clear by Corollary 3.19.

Bulletin of Mathematical Sciences

By Corollary 3.2, is a singleton.

Journal of Inequalities and Applications

By Corollary 2.3, we arrive at (3.2).

Journal of Inequalities and Applications

By Corollary 4.2, the solution is unique.

Advances in Difference Equations

By Corollary 3.3, we have for all.

Advances in Difference Equations

Thus, Corollary 2 holds by Corollary 1.

Advances in Difference Equations

By Corollary 3.4, for any and, (4.4).

Fixed Point Theory and Applications

By Corollary 11, D is Meir-Keeler.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When using "by corollary", ensure the statement it introduces is a direct and easily understood consequence of the preceding statement. Avoid using it for conclusions that require significant additional explanation.

Common error

Avoid using "by corollary" to introduce a point that is only tangentially related to the previous statement. A corollary should be a clear and immediate deduction, not a separate or weakly connected idea.

Linguistic Context

The phrase "by corollary" functions as an adverbial phrase introducing a statement that is a direct and immediate consequence of a preceding theorem or proposition. It indicates a logical deduction. Ludwig AI supports this analysis showing the uses in different scientific and mathematical papers.

Expression frequency: Very common

Frequent in

Science

95%

Formal & Business

3%

News & Media

1%

Less common in

Academia

1%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "by corollary" is a grammatically correct and frequently used phrase, predominantly in scientific and mathematical writing, to introduce a statement that directly and logically follows from a previously established result. As Ludwig AI confirms, its primary function is to assert a clear, immediate deduction. When employing "by corollary", ensure the connection between the preceding statement and the introduced consequence is evident. While appropriate in formal contexts, simpler alternatives may be preferable in informal writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

it follows that

This phrase directly indicates a logical consequence or conclusion.

consequently

This adverb emphasizes that something happens as a result of something else.

therefore

A common term to show a logical conclusion based on prior statements.

as a consequence

Highlights the result or effect of a preceding action or statement.

hence

Indicates a logical inference or conclusion.

it can be deduced that

Emphasizes the act of deriving a conclusion through reasoning.

it logically follows

Highlights the logical connection between premises and conclusion.

in consequence of

Shows a cause-and-effect relationship more formally.

in light of that

Introduces a conclusion based on previously mentioned information.

accordingly

Indicates that an action or state is appropriate or logical based on what precedes it.

FAQs

How is "by corollary" used in academic writing?

"By corollary" is used to introduce a statement that logically follows from a previously proven theorem or proposition. It's common in scientific and mathematical contexts to present immediate consequences of established results.

What are some alternatives to "by corollary"?

You can use alternatives like "it follows that", "consequently", or "therefore" to indicate a logical consequence or conclusion.

Is it appropriate to use "by corollary" in informal writing?

While grammatically correct, "by corollary" is more suited to formal and academic writing. In informal contexts, simpler alternatives like "so" or "therefore" might be more appropriate.

How does "by corollary" differ from "by implication"?

"By corollary" indicates a direct and immediate consequence of a proven statement, while "by implication" suggests a more indirect or inferred conclusion that isn't explicitly stated but can be reasonably deduced.