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Frannas
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Why is 0! = 1?
All proofs have at their basis a set of axioms&definitions, and a proof is simply to show that something else follows from those very same axioms&definitions.Frannas said:Is there no proof to that?
fourier jr said:n! is the number of possible ways to scramble up n objects & there's only one way to scramble up zero objects. It's a bit similar to showing there's only one empty set; if there were another way, what would it look like?
The factorial of a number is the product of all the positive integers from 1 to that number. Therefore, 0 factorial is defined as 1.
The value of 0 factorial being equal to 1 is a convention adopted by mathematicians. It is based on the properties of the factorial function and makes mathematical equations and expressions simpler to write and understand.
Yes, there are several ways to prove that 0 factorial is equal to 1. One way is to use the definition of factorial and the concept of empty product, where multiplying any number of elements results in 1. Another way is to use mathematical induction to show that the formula for factorial holds true for 0.
Knowing that 0 factorial is equal to 1 is important in various mathematical concepts and equations. It allows for the simplification of equations and helps in solving problems involving permutations, combinations, and binomial coefficients.
No, 0 factorial is not the only number equal to 1. Any number raised to the power of 0 is also equal to 1. In addition, the number 1 itself is equal to 1. However, 0 factorial is unique in that it is the only factorial that equals 1.