giai thừa
Definition
- Noun (Mathematics):
- Factorial: A mathematical function denoted by an exclamation mark (!) after a non-negative integer. It is the product of all positive integers less than or equal to that integer. For example, the factorial of 5 (written as 5!) is calculated as 5 × 4 × 3 × 2 × 1 = 120. By definition, the factorial of 0 is 1.
Usage Examples
- Noun:
- Giai thừa của 4 là 24. (The factorial of 4 is 24.)
- Trong xác suất, chúng ta thường xuyên sử dụng phép tính giai thừa. (In probability, we frequently use factorial calculations.)
- Ký hiệu "n!" được đọc là "n giai thừa". (The symbol "n!" is read as "n factorial.")
Advanced Usage
- Double Factorial (Giai thừa kép): Denoted by two exclamation marks (n!!), it is the product of all integers from 1 to n that have the same parity (odd or even) as n.
- Giai thừa kép của 7 (7!!) là 7 × 5 × 3 × 1 = 105. (The double factorial of 7 (7!!) is 7 × 5 × 3 × 1 = 105.)
Variants and Related Words
Hàm giai thừa (n): factorial function.
- Hàm giai thừa tăng trưởng rất nhanh. (The factorial function grows very rapidly.)
Giai thừa nguyên tố (n): primorial, a function denoted as n# which is the product of all prime numbers less than or equal to n.
- Giai thừa nguyên tố của 5 là 5 × 3 × 2 = 30. (The primorial of 5 is 5 × 3 × 2 = 30.)
Synonyms
- Factorial: The direct and only standard English equivalent for the mathematical term "giai thừa."
Related Concepts (Not Idioms)
Permutation (Hoán vị): The number of ways to arrange 'n' distinct objects is n! (n factorial).
- Số hoán vị của 3 vật thể là 3 giai thừa, tức là 6. (The number of permutations of 3 objects is 3 factorial, which is 6.)
Combination (Tổ hợp): The binomial coefficient, which uses factorials in its formula: n! / [k!(n-k)!].
- Công thức tổ hợp có chứa các phép tính giai thừa. (The combination formula contains factorial calculations.)