Corollary definitions
| Word backwards | yralloroc |
|---|---|
| Part of speech | Noun |
| Syllabic division | Co-rol-la-ry |
| Plural | The plural form of the word "corollary" is "corollaries." |
| Total letters | 9 |
| Vogais (2) | o,a |
| Consonants (4) | c,r,l,y |
Understanding the Corollary
Definition:
A corollary is a proposition that follows from another one that has already been proven. Essentially, it is a logical consequence or inference deduced from a theorem or principle.
Usage in Mathematics:
In mathematics, corollaries are commonly used to extend the implications of a theorem or provide further insights into a particular concept. They help to solidify the understanding of the main result and showcase its broader application.
Relationship with Theorems:
Corollaries are closely related to theorems, with the key difference being that theorems are primary results that require proof, while corollaries are immediate consequences derived from those proved results. Think of corollaries as additional information that naturally follows from a theorem.
Significance in Logic:
Corollaries play a crucial role in logic and reasoning. They demonstrate the interconnected nature of mathematical concepts and help build a coherent framework of knowledge. By establishing corollaries, mathematicians can advance their understanding and solve complex problems more effectively.
Example:
For example, if a theorem states that "All right angles are equal," a corollary to this theorem could be "In a triangle, the sum of interior angles is 180 degrees." This corollary directly follows from the theorem and provides additional information about the properties of angles.
Conclusion:
Corollaries are valuable tools in mathematics, logic, and various other fields where deductive reasoning is employed. By grasping the concept of corollaries and their relationship with theorems, individuals can deepen their understanding of fundamental principles and their interconnectedness.
Corollary Examples
- The first corollary of the new policy is increased employee satisfaction.
- As a corollary to his success, he was promoted to a higher position.
- One corollary to the theory is the need for further research.
- The corollary of hard work is often success.
- Her dedication to her craft was a corollary of her passion for music.
- A corollary to the new law is reduced crime rates.
- As a corollary to the new technology, our processes have become more efficient.
- One corollary of the pandemic is the increased focus on healthcare systems.
- The corollary of teamwork is often increased productivity.
- His commitment to excellence was a corollary of his dedication to his work.