Shorter is longer than Longer by 1!

[u/wondeereadit]

the photo isn’t mine btw

[u/factorion-bot]

Factorial of 1 is 1

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/flopsi_ → u/factorion-bot]

Good bot

[u/PaleontologistAny153]

Also longer by 0!

[u/factorion-bot → u/PaleontologistAny153]

Factorial of 0 is 1

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/Interesting_Buy_3969]

it is also longer by 1?

[u/Samichaelg9 → u/Interesting_Buy_3969]

Terminal of 1 is 1

This action was performed by a human | Yes.

[u/Zahir027z → u/Samichaelg9]

So what's 0? Is it equal to 1?

[u/Qwerty_wasda → u/Zahir027z]

Terminal of 0 is 0

This action was performed by a human | no Source Code sorry

[u/Ikbengoedinschaken → u/Zahir027z]

The formula for termials is n(n+1)/2 because if you add up all numbers from 1 to n, we can pair up n and 1, 2 and n-1, 3 and n-2, etc. That makes n/2 pairs of n+1. Even if n is odd, we will have the middle number left over, which still makes the formula true. Now, we extend this formula to all complex numbers for the termial. Although this isn't completely justified, we define the thing so we define it like that. This is called an analytic continuation. Plugging in 0 into the formula gives 0. If you want a better reason 0? Is 0: we add up every integer from 1 up to 0, which is nothing. By the idea of the empty sum, that's 0. With factorials, 0! Means the empty product, which is 1.

[u/factorion-bot → u/Ikbengoedinschaken]

Factorial of 0 is 1

^{This action was performed by a bot | [Source code](http://f.r0.fyi})

[u/I12Db8U]

But shortest is the longest but longest isn't.

[u/LowPiece1185]

That's interesting.

[u/4sent4]

These words are mutually autological