User blog:Bubby3/The fastest-growing function ever devised!

Did you know that Zeno was actually right when he came up with Zeno's paradox! That's right, Achilies will never overtake the tortoise. That means that a faster object can never overtake a slower object, so a beam of light cannot overtake a tortoise, no matter how much time has passed!

And you wonder why all of this is going on, why can something never overtake something else, despite going faster. The reason is that the series 1/(n^x) will NEVER converge, no matter what value n is! In fact, no sum ever will converge, so even the sum 1/SAM(n), where SAM(n) is a Sam function, will diverge, although ridiculously slow. You can't even describe how slow the divergence is!

You want to know why no infinite sum convegres, do you? In fact, we recently discovered that it comes from a super-powered form of dark energy, known as hyper dark energy, that even affects abstract concepts, including our real number line. It does that by stretching the difference betweenreal numbers by aa very time amount. Hyper-dark energy is also responsible for a vareity of previously unknown phonenomena, including Easter bunnies, Complex BEAF, and the ripping of spacetime dimensions.

You want to know why mathematicians haven't noticed the effect of hyper dark energy on the real numbers until now? The reason is that the effect is so small that no mathematican can describe it, despite that it existed since the very beginning of time. The effect is so small that not even the reciprocal of Sam functions can describe it.

How can all of this be made into a large number function? We can make a hierarchy similar to the FGH but much faster growing hierarchy called the Divergence Hierarchy (DH for short). Here's how it works.


 * D0(n) = 2n
 * Da+1(n) = \(\min_{i} \Bigg( \sum_{m=1}^i \frac{1}{D_a(m)} \Bigg) > n\)
 * Da(n) = Da[n](n) if n is a limit ordinal

That definition might look a bit mysterious. The first rule is the base case, defining D0(n) to be 2 to the power of n. The second rule is where the hierarchy gets its power from. What it is saying is that you find the smallest i for that the sum of the reciprocal of Da(m) where m is from 1 to i is greater than n. The third rule just takes the fundamental sequences of the ordinals, which lets it go to transfinite ordinals.

Here is an analysis of the hierarchy.

You would wonder why this function grows faster than Little Biggedon, and thus is uncomputable. The answer is the prescion in the terms of 1/2^n grow uncoumutably fast, so the function is uncomputable.
 * \(D_1(n)\) grows absurdly faster than Little Biggedon, and even Sasquatch.
 * \(D_\omega(n)\) is comparable to ometochtli(n)
 * \(D_{\varepsilon_0}(n)\) is the limit of Ultimate BEAF.
 * \(D_{\phi(\omega,0)}(n)\) is the limit of Binary Notation defined here.
 * \(D_{\omega^{CK}_1}(n)\) is comparable to a Sam function.

We can go much farther by making a function which counts the catching points between the FGH and the DH, or the values of a where Da(n) has the same growth rate as fa(n). I call this function CD(n). In fact, the ordinal CD(K) (where K is the weakly compact cardinal) is so large it breaks all laws of physics ever created by anyone just by existing. Why is this true? A catching-point between the DH and FGH creates a wormhole in ordinal-space, and weakly compact cardinals in OCFs create hyperdense structures, and every law of physics ever created says that wormholes cannot be in hyperdense structures, because of the very simple laws of physics by our intution. So that means we need to overhaul potentially all of physics just to support some very large ordinal. No one, not even the smartest people have ever imgained that to be true!

In the end, the existence of hyper dark matter was thought to only have extremely minor cosequences, but the conseqeucnes actuallly require a complete overhaul of potientally all of physics! The lesson is that when something has an extremely minor effect, it could have an extremely major effect by measuring how minor the effect is!

'''Just kidding! Happy April fools day! '''I hope you had a good laugh out of that joke I came up and I waited for today just to post.