vô nghiệm
Definition
- Adjective (Mathematics):
- Having no solution: Describes an equation or inequality for which no value of the variable satisfies the condition. The solution set is empty.
- Unsatisfiable: Indicates that a given mathematical statement or condition cannot be true for any value within the considered domain.
Usage Examples
- Adjective:
- Phương trình đó là vô nghiệm. (That equation has no solution.)
- Bất phương trình trở nên vô nghiệm sau khi biến đổi. (The inequality becomes unsatisfiable after the transformation.)
- Nếu delta nhỏ hơn 0, phương trình bậc hai là vô nghiệm. (If the discriminant is less than 0, the quadratic equation has no real solution.)
Advanced Usage
- The term is primarily used in formal mathematical contexts (algebra, calculus) to describe the property of an equation or system of equations.
- It can be used in a more figurative, technical sense outside of pure mathematics to describe a problem or situation with no possible answer or resolution.
Variants and Related Words
- Nghiệm (n): Solution (of an equation).
- Tìm nghiệm của phương trình. (Find the solution(s) of the equation.)
- Có nghiệm (adj): Having a solution(s).
- Phương trình này có nghiệm duy nhất. (This equation has a unique solution.)
Synonyms
- Unsatisfiable
- Insolvable (in the specific context of having no solution)
- Solutionless
Related Terms and Phrases
- Tập nghiệm rỗng: Empty solution set. This is the formal result of an equation being .
- Phương trình vô nghiệm có tập nghiệm rỗng. (An equation with no solution has an empty solution set.)
- Vô số nghiệm: Having infinitely many solutions (the conceptual opposite in terms of solution set size).
- Không phải vô nghiệm mà là vô số nghiệm. (It's not that it has no solution; it has infinitely many solutions.)