Cutting them off

Number Theory Level 1

0 ! 0 ! = ? \LARGE \frac{0!}{0!} = \ ?


The answer is 1.

Sifat Shishir by Sifat Shishir , 27, Bangladesh

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4 solutions

Sravanth C.
Jun 27, 2015
  • We can express, ( n − 1 ) ! = n ! n (n-1)!=\dfrac{n!}{n} . Let's put the value of n = 1 n=1

( 1 − 1 ) ! = 1 ! 1 0 ! = 1 ! 0 ! = 1 (1-1)!=\dfrac{1!}{1} \\ 0!=1! \\ \boxed{0!=1}

  • Now, we are asked: 0 ! 0 ! = 1 1 = 1 \dfrac{0!}{0!} = \dfrac11 \\ =\boxed1
5 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Simple standard approach.

Adarsh Mahor
Jul 16, 2015

n!/n! =1 SO, 0!/0! =1 So its very simple

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Hunter Handley
Jul 20, 2015

Just think, anything times 1 is itself. If “a” stood in for 0!, that means 1a=1 or 1(0!)=0!, which is true

0 Helpful 0 Interesting 0 Brilliant 0 Confused

not quite :

1 times 0 = 0, all rigth , but 2 times 0 = 0 as well , and 3.1416 times 0 = 0 ....... so??

Luis Carlos Garcia Sr - 5 years, 8 months ago
Samar Singh
Jul 10, 2015

0!=1 So. 0!/0!=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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