0! = ?(surprising solution)

Algebra Level 1

Zero factorial is equal to what number?

Hint 1: It doesn’t equal an indeterminate number.

Hint 2: 5! = $\frac{6!}{6}$ = 120

Note: 5! = 5 x 4 x 3 x 2 x 1

Indeterminate 0 1 Infinity

2 solutions

Mohammad Khaza
Nov 2, 2017

proof:

$1!=1 \times 1=1$

$2!=1 \times2=2$

$3!=1 \times 2 \times 3=6$

$4!= 1\times 2 \times 3 \times 4=24$

so, we can say that, $n!=1 \times 2 \times 3 \times (n-2) \times (n-1) \times n$

and so, logically we can say that , $n!=n(n-1)!$ ..............[1]

now, putting $(n=1)$ in equation [1] ,we get ,

$1!=1 \times 0!$

or, $1=0!$ .....................d.

That is a very clever formula. It makes my solution seem almost childish! Nicely done.

Fresh 750 - 3 years, 7 months ago

thanks bro!. this not factorial ,this is exclamatory sign. (just joking.)

Mohammad Khaza - 3 years, 7 months ago

Fresh 750
Nov 2, 2017

5! = $\frac{6!}{6}$ = 120

4! = $\frac{5!}{5}$ = 24

3! = $\frac{4!}{4}$ = 6

2! = $\frac{3!}{3}$ = 2

1! = $\frac{2!}{2}$ = 1

0! = $\frac{1!}{1}$ = $\frac{1}{1}$ = 1

0! = 1

–1! = $\frac{0!}{0}$ = $\frac{1}{0}$ = indeterminate