It's because $n! = \prod_{0<k\le n} k.$ ($n!$ is the product of all numbers $1, 2,\dots n$) For $n = 0$ there isn't any number greater then 0 and lesser or equal to $n$, so the product is empty; the empty product is defined by convention as 1.

2024年5月17日 · The first reason why zero factorial is equal to one is that the definition of the factorial states that 0! = 1. A definition is a mathematically correct explanation (even if a somewhat unsatisfying one).

Simple answer: 0! (read "Zero Factorial") is defined to equal 1. Involved answer(s): There are several proofs that have been offered to support this common definition. Example (1) If n! is defined as the product of all positive integers from 1 to n, then: 1! = 1*1 = 1 2! = 1*2 = 2 3! = 1*2*3 = 6 4! = 1*2*3*4 = 24... n! = 1*2*3*...*(n-2)*(n-1)*n ...

2023年7月28日 · Because “nothing” behaves differently than “something”, operations with it can be surprising. Although students learn that \(x^0=1\) for any non-zero number x, they often wonder, why?? I’ve selected a few out of at least a dozen such questions in our archive. Using the quotient rule for exponents. We’ll start with a question from 1996:

2023年8月11日 · Why does 0! = 1? Is there a reason or is this like anything to the power of 0 = 1 - there is not a reason? Recall that “factorial” means the product of descending integers, and is written as \(n!=n(n-1)(n-2)\dots1\). For example, \(5!=5\cdot4\cdot3\cdot2\cdot1=120\).

2023年10月4日 · Mathematically proving that the factorial of 0 is equal to 1 is based on the definition of the factorial function and follows the convention used in mathematics. The factorial function is typically defined as follows: n! = n × (n – 1) × (n – 2) × … × 2 × 1.

Zero to the power of zero, denoted as 00, is a mathematical expression with different interpretations depending on the context. In certain areas of mathematics, such as combinatorics and algebra, 00 is conventionally defined as 1 because this assignment simplifies many formulas and ensures consistency in operations involving exponents.

2024年8月2日 · Explore the concept of zero factorial (0!0!) in mathematics. Learn about the definition of factorial, how it is calculated, and the derivation of 0!=1. Understand the significance of zero factorial and its applications, along with examples and frequently asked questions related to factorial calculations.

Why some people say it's 0: Zero divided by any number is 0. Why some people say it's 1: A number divided by itself is 1. Only one of these explanations is valid, and choosing the other explanations can lead to serious contradictions.

So yes, 0! = 1 is correct because mathematicians agreed to define it that way (nothing more and nothing less) in order to be consistent with the rest of mathematics. Discover why zero factorial is equal to 1 - uncover the truth behind a seemingly absurd statement and learn why it's true.