factorials are mostly encountered in combinatorics, which is problems like, how many ways are there to put 3 objects of different colors in a row? well, the first can be any of the 3, the second can be either of the other 2, and the last is whichever 1 is left, so 3×2×1=3!=6
so how many ways are there to put 0 objects in a row? well there’s 1, it’s this one:
factorials are mostly encountered in combinatorics, which is problems like, how many ways are there to put 3 objects of different colors in a row? well, the first can be any of the 3, the second can be either of the other 2, and the last is whichever 1 is left, so 3×2×1=3!=6
so how many ways are there to put 0 objects in a row? well there’s 1, it’s this one:
that’s why 0!=1
Wow, that was a really great explanation! Thanks! I could have needed this twenty years ago and maybe we wouldn’t have had this interaction.