+870 0! equals 1;
One of the ways to show this is to "complete the pattern":
$$\\5!=1\times 2\times 3\times 4\times 5=120
\\4!=\frac{5!}{5}=\frac{120}{5}=24
\\3!=\frac{4!}{4}=\frac{24}{4}=6
\\2!=\frac{3!}{3}=\frac{6}{3}=2
\\1!=\frac{2!}{2}=\frac{2}{2}=1
\\0!=\frac{1!}{1}=\frac{1}{1}=1$$
But that's where the pattern ends; you can't continue, because you end up with this:
$$(-1)!=\frac{0!}{0}=\textcolor[rgb]{1,0,0}{\frac{1}{0}}$$
See what I mean ?
+870 0! equals 1;
One of the ways to show this is to "complete the pattern":
$$\\5!=1\times 2\times 3\times 4\times 5=120
\\4!=\frac{5!}{5}=\frac{120}{5}=24
\\3!=\frac{4!}{4}=\frac{24}{4}=6
\\2!=\frac{3!}{3}=\frac{6}{3}=2
\\1!=\frac{2!}{2}=\frac{2}{2}=1
\\0!=\frac{1!}{1}=\frac{1}{1}=1$$
But that's where the pattern ends; you can't continue, because you end up with this:
$$(-1)!=\frac{0!}{0}=\textcolor[rgb]{1,0,0}{\frac{1}{0}}$$
See what I mean ?
