Why does zero factorial is equal to one?

n! = n * (n-1) ! Interchange LHS and RHS n * (n 1) ! = n! (n-1) ! = n! /n substituting n = 1 (1-1)! = 1! / 1 0! = 1 / 1 = 1 A: By Ducnhuandoan Onother proof is: A Schema Proof Without Words That Zero Factorial Is Equal To One. 6! = 720 = 1*76 -6*66 +15*56 -20*46 +15*36 -6*26 +1*16. 5! = 120 = 1*65 -5*55 +10*45 -10*35 + 5*25 -1*15. 4! = ..24 = 1*54 -4*44 + 6*34 - 4*24 + 1*14. 3! = ....6 = 1*43 -3*33 + 3*23 - 1*13. 2! = ....2 = 1*32 -2*22 + 1*12. 1! = ....1 = 1*21 -1*11. 0! = … ..= 1*10. 0! =... ....= 1*10 = 1*1 = 1. Conclusion 0!=1 The proof "without Words" above that zero factorial is equal to one is a New that: *One has not to accept by convention 0!=1 anymore. *Zero factorial is not an empty product. *This Schema leads to a Law of Factorial. Invention's Author: Ducnhuandoan (Đoàn Đức Nhuận by vietnamese) By clicking Ducnhuandoan or LawsfromABCMaths on any searching tool on internet you can see more about my easymath.