Prove that 0! = 1
(please solve with explanation)

• n! = n*(n-1)*(n-2)*(n-3)*....*3*2*1
  
  The above formula can be written as
  n! = n*(n-1)!, then
  
  (n-1)! = n!/n
  
  Put n=1, then 0! = 1!/1 = 1
• 10 years agoHelpfull: Yes(5) No(1)
• as n!=n*(n-1)*....*1;
  so n!=n*(n-1)!
  hence n!/(n-1)!=n;
  put n=1;
  so 1!/(1-1)!=1;
  1!/0!=1;
  1!/1=0! so 0!=1 hence proved
• 10 years agoHelpfull: Yes(2) No(0)
• Usually n factorial is defined in the following way:
  
  n! = 1*2*3*...*n
  But this definition does not give a value for 0 factorial, so a natural question is: what is the value here of 0! ?
  
  A first way to see that 0! = 1 is by working backward. We know that:
  
  1! = 1
  2! = 1!*2
  2! = 2
  3! = 2!*3
  3! = 6
  4! = 3!*4
  4! = 24
  
  
  We can turn this around:
  4! = 24
  3! = 4!/4
  3! = 6
  2! = 3!/3
  2! = 2
  1! = 2!/2
  1! = 1
  0! = 1!/1
  0! = 1
• 10 years agoHelpfull: Yes(1) No(3)
• (n-1)! = n!/n
  0!=1!/1
  1!=2!/2
  and so on ...........
• 10 years agoHelpfull: Yes(0) No(0)