"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
so to confirm episode 2a will not be published. it will be done AFTER my next scene, and i will post the results on my next scene. Blue: 100 (immune), Purple: 50 (immune), Orange: 30 (immune), Lime: 15 (immune), White: 10 (immune), Yellow: 5 (immune), Red: 3 (eliminated). Episode 2a will be a team event.
Blue, Orange, and White are on Team 10066100 and Purple, Lime, and Yellow are on Team 150100100. The event is a marble race. On the end Team 10066100 wins.
Event Rules:
Complete the marble race as fast as possible.
Stakes:
+50 for winning team
+0 for losing team
Results:
Team 10066100 wins
Team 150100100 loses
Leaderboard:
Blue [150] IMMUNE
Orange [80] IMMUNE
White [60] 1.944%
Purple [50] 6.111%
Lime [15] 38.333%
Yellow [5] 53.611%
Red [3] ELIMINATED
Nobody was eliminated because it was a team event. BUT Day 2b will have an elimination with 1 person eliminated.
As for Geometry Actions part, you have to right-click (if you use left-click for clicking) the object you want and then go to the "geometry actions" thing.
Our emotionally invested salmon is basically a walking (swimming?) conspiracy subreddit. He’s got the receipts, the zoomed-in screenshots, and maybe even a crustacean witness on stand-by.