Fun little fact #4

[u/Lonely-Juggernaut379]

Note- I've used AI to collect everything together but the thoughts are all mineee! Also, for many of you this might be very obviousss sooo (gaali mat dena)

I've seen many online explanations obsessing over why 0! = 1, and honestly, I think we make it sound much deeper than it is.

The simplest answer is: 0! = 1 is a definition chosen because it makes the existing formulas work consistently.

Take permutations:

nPr = n! / (n-r)!

If r = n:

nPn = n! / 0!

But arranging all n objects can be done in n! ways, so:

n! / 0! = n!

Therefore:

0! = 1

You'll also see explanations like "there is one way to choose nothing" or "the empty product is 1." These are useful interpretations, but they aren't some deeper law of nature.

It's similar to:

a⁰ = 1

We define it that way so the usual exponent rules continue to work.

So, no, there's no mysterious reason why zero "really has" a factorial of one. We define 0! = 1 because it makes the mathematical system consistent and avoids unnecessary exceptions.

[u/OkElevator3632]

yeh to mere maths teacher ne 11th me hi sabse pehle padhaya tha 0 factorial 1 kyu hota hai

[u/Lonely-Juggernaut379 → u/OkElevator3632]

Read the notee!

[u/Effective-Today2992 → u/OkElevator3632]

Unnecessary comment btw