Zero Factorial is One: Go Patterny!

You might have heard of some proofs.
What though if we come up with a pattern?

4!
=4•3•2•1
=5•4•3•2•1/5
=5!/5

3!
=4•3•2•1/4
=4!/4

2!
=3•2•1/3
=3!/3

1!
=2•1/2
=2!/2

0!
=1/1
=1!/1
=1