Algodoo

Little oopsie you made there: You see, 0! is actually 1.

Actually, factorials are defined by: gamma(n+1). gamma(0+1) is 1, so 0! is 1.

NOT TRUE

0x1=1 Which means zero factorial equals zero and that is final

Yeah, and also if you’re having problem like if you’re having a problem with it, read the spoiler alert in zero factorials word bubble

anything mutiplyed by 0 is 0. so 0x1=0.

If U try negative fatorials, U will have an error. negative fatorials will give U an INVALID INPUT.

Yeah, that’s what I put 0×0 like I put 0×1 = 0 but it just like it just put in one instead of zero

-1!=I I=imaginary number

"The gamma function, denoted as Γ(x), is like the factorial function’s cooler, more complex cousin. It extends the idea of factorials to non-integer values. For positive integers, Γ(n) = (n – 1)! — neat, right?

But when you ask for Γ(0)...

THE DRAMA AT ZERO

Γ(0) is undefined because the gamma function has a pole at zero. That means it blows up to infinity there — like trying to divide by zero but with extra flair.

Mathematically, as x → 0⁺, Γ(x) behaves like 1/x – γ + ..., where γ is the Euler–Mascheroni constant. So yeah, it goes kaboom

IN NERDSPEAK

\lim_{x \to 0^+} \Gamma(x) = \infty

So asking for Γ(0) is like asking “What’s the flavor of a black hole?” — it’s undefined, but you know it’s intense." - AI

"-1! is undefined — and not just because math decided to be dramatic. The factorial function, which normally goes like n! = n × (n–1) × (n–2) × ... × 1, only works for non-negative integers. So when you ask for -1!, math basically says: 'Nope. That’s illegal.'

WHY IT BREAKS

The factorial relies on multiplying down to 1. But how do you multiply down from –1? You’d be stuck in an infinite loop of negativity.

The recursive definition n! = n × (n–1)! leads to a contradiction if you try to plug in –1. You’d end up needing to divide by zero, which is a big mathematical no-no

GAMMA FUNCTION TO THE RESCUE?

The Gamma function extends factorials to non-integer values, like 3.5!, but it has poles (infinities) at negative integers, including –1. So:

Γ(-1 + 1) = undefined (infinite)

So yeah, –1! = Γ(0) = ∞, which is math’s way of saying 'don’t go there'.

TL;DR:

You: Hey math, what’s '–1!'?
Math: I’m not mad… I’m just disappointed." - AI

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