Corollary: meaning, definitions and examples
๐
corollary
[kษหrษl.ษ.ri ]
Definition
mathematics, logic
A corollary is a statement that follows readily from a previous statement or proposition that has been proven. It is often considered an easy or obvious consequence that requires little additional proof because it is logically derived from established results. Corollaries provide insight and additional information about the original statement, and they are frequently used in mathematical and logical contexts. For example, if a theorem is proved, a corollary can be easily inferred from that theorem without extensive additional research.
Synonyms
consequence, implication, outcome, result.
Examples of usage
- The triangle inequality is a corollary of the properties of absolute values.
- From the theorem, we can derive a corollary that simplifies our calculations.
- The corollary states that with the assumptions made, the following must also be true.
Interesting Facts
Etymology
- The word comes from the Latin 'corollarium', meaning 'a small crown', which suggests something that follows from or is added to what is already there.
- First recorded use in English was in the 14th century, indicating a long history of the term in academic language.
- Corollary originally referred to something that was 'added on', just like a decorative piece added to a crown.
Mathematics
- In mathematics, a corollary is a theorem that follows easily from a previous theorem, serving as a way to build on existing knowledge.
- Famous corollaries often simplify complex ideas, making them easier to understand and apply.
- An example includes the corollary that states if a triangle is right-angled, then the Pythagorean theorem applies.
Philosophy
- In philosophical discussions, a corollary can be used to derive further implications or consequences from a primary argument.
- This helps in constructing logical frameworks where one assertion leads to another, enriching the debate.
- Philosophers like Aristotle often employed corollaries in their argumentation to illustrate points clearly and logically.
Psychology
- In psychology, a corollary can be understood as the mental processes and subsequent behavior that result from a given thought or belief.
- George Kelly's personal construct theory discusses corollaries as ways that individuals interpret experiences based on previous outcomes.
- Corollary thinking emphasizes the connection between experiences and how they can lead to similar future reactions.
Legal Context
- In law, a corollary may refer to principles that follow from established legal precedents to provide clarity in cases.
- Lawyers often cite corollaries in reasoning to support their arguments, basing conclusions on what has been previously agreed upon.
- Understanding legal corollaries helps in predicting outcomes in court based on past rulings.
Translations
Translations of the word "corollary" in other languages:
๐ต๐น corolรกrio
๐ฎ๐ณ เคเคชเคธเคเคนเคพเคฐ
๐ฉ๐ช Korollar
๐ฎ๐ฉ korolari
๐บ๐ฆ ะบะพัะพะปัั
๐ต๐ฑ korolarny
๐ฏ๐ต ่ฃ้ก
๐ซ๐ท corollaire
๐ช๐ธ corolario
๐น๐ท korolarya
๐ฐ๐ท ๋ถ๊ฐ๋ช ์
๐ธ๐ฆ ูุชูุฌุฉ
๐จ๐ฟ korolรกล
๐ธ๐ฐ korolรกr
๐จ๐ณ ๆจ่ฎบ
๐ธ๐ฎ korolar
๐ฎ๐ธ afleiรฐing
๐ฐ๐ฟ าะพััััะฝะดั
๐ฌ๐ช แแแ แแแแ แ
๐ฆ๐ฟ korolyar
๐ฒ๐ฝ corolario
Word Frequency Rank
At position #12,991, this word is part of sophisticated English vocabulary. It's useful for academic or professional contexts where precise language is needed.
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- 12988 veiled
- 12989 forefront
- 12990 subsidence
- 12991 corollary
- 12992 masculinity
- 12993 subunit
- 12994 repealing
- ...