★266
"If I were to number all the Drops from 1,2,3,4,5... transfinite up to infinite, I'll have everything real numbers present."
He turned, his full attention on me as I continued.
"However, real numbers can't reach true infinity. Because after each last number, you realise you can add one and get back on the track. So from that, I can take the power set of each number to create more and more sets."
For example; the power set of Drop 1,2 & 3. I can have (),(1),(2),(3),(1.2),(1.3), and so on. Imagine using a power set of infinite real numbers.
"The Power Set of the Drops equals the Continuum which equals the Ocean of All Possible Drops. That's Above Aleph Null."
He chuckled, which was clear this time around. He's interested in hearing me our.
"In the future, a structure called Superworld will be created for the lesser Stars."
"How about a power set of Aleph Null?"
"The Continuum is already above Aleph Null. According to the Continuum Hypothesis, if there exists an infinite between (ℵ₀) & (2^ℵ₀), then, we may be talking about Aleph One(ℵ₁). However, if there's no infinite between the two, it's below (ℵ₁) yet above (ℵ₀). It's still low."
He raised a finger and gently shook it, a quiet gesture that carried more certainty than any words.
"Not even close."
"Ok."
I paused briefly, already finding a way out within that silence.
"With the help of an axiom, I can create more."
I said, determining to prove the laws of man are indeed capable of dictating the cosmic carpet of a god.
"I can take all the ordinals and add something else. For example,
1,2,3,...,
1+a,2+a,3+a,...,
1a×2,2a×2,3a×2,...,
1a²,2a²,3a²,...,
1a³,2a³,3a³,...,
1a^a,2a^a,3a^a,...,and so on.
I can keep going past mathematical notations without end, but something still comes behind all of these. I'll call it ω₁. Now, ω₁ is going to have more cardinals compared to (ℵ₀). So, the cardinal number describing things in order in relation to ω₁ is (ℵ₁)."
"Finally."
He said, his voice in whispers.
"Also, with the help of an axiom,"
I continued, trying my best to block the road.
"I can use the previous ordinals to go past regular Alephs Omega (ℵω) which is not the end as it can be used to construct more Alephs like (ℵω ², ℵω ³...)and it goes on.
With the cardinality of Aleph Omega |ℵω| still (ℵω). By utilising power sets once again, P(ℵω) = 2ℵω which is bigger than (ℵω).
The thing is, with the help of an axiom and power setting, no infinity is infinite. Because cardinal (κ) has (2^κ > κ) and so on. Forgive me for talking on par with you. I'm ready for any punishment. "
I lowered my head in silence, waiting.
"I'm enjoying this... there's more, right? Spill them out."
He said his voice was almost playful.
"Indeed."
I rose and continued.
"With the help of an axiom, I can assume there's an end where no amount of power setting can get me there. (ℵ₀ → continuum → ℵ₁ → ℵω → beyond), until they reach something that even infinite power can't touch, an inaccessible horizon. Mathematically, it's called an inaccessible cardinal."
I lowered my head once again, and what followed was a round of applause from my creator.
"Fantastic."
He spoke as the sound of his applause echoed around us, reverberating through the space.
"This is what I've always wanted ever since I decided to create you. I don't want a mindless child who treats me as a god. I need a child who can make me think twice, challenge me, and give me his thoughts. You're my finest creation, Acamar, I'm so proud."
I was surprised at his words, but now that I know what he wants, I'll do all I can to keep this spot.
"So, did my stubbornness go through?"
"My Worlds are absolute. So, you failed."
He said.
"Although you saved me some explanation about their ontological superiority. The Laws will be created based on your opinion. Of all the things you said, the last part carried the most weight, and it's the same Law that'll be applied in the Hyperworlds."
"Information for the future..."
He descended without a reply, and I followed. We were approaching a Drop, which I was surprised at how big they were. We passed through the transparent barrier, and he stopped.
"These are Hyperworlds."
He said, but I saw nothing. I can feel the energy, but nothing appears physical.
"Each Drop has a unique way of housing a Nest. The Nest in here exists parallel with this Drop."
I thought for a moment trying to match the pieces with a need for explanation.
"Exist parallel to this Drop."
I murmured to myself. He snapped his fingers, and we appeared in the parallel dimension that housed the Nest. He needed not snap to get us down here, but he did.
Countless worlds, Hyperworlds, can be seen floating freely.
"This entire dimension is the Nest ev..."
"Even though dimensionality is irrelevant in the Drop."
I finished his sentence, and he nodded.
"There's a difference between no Concept, transcend Concept and predate Concept. We'll use time as an example
Lacking conceptions means that it has no. Therefore, time itself is not a factor in the world. It's considered non-existent. An example is creating a world without the said concept. This can be grouped into two, the ability to lack conceptions, but one be created and the other is complete irrelevance.
To transcend time means time doesn't exist, and if it does, the world will be free from its constraints. An example is living in the human world, but one is unaffected when time is stopped. It takes a time transcendent being to do the first two.
Lastly, it is the predating concept of time. It means the realm or person existed before time came into play, making them naturally superior to it. An example of such a realm is the Abyss & Divine Land.
As for you, the one who I gave my inheritance, you've predated not transcend all that I have predated, but these powers won't surface immediately. The same thing with the information. You won't be able to understand most of them, but later on, you will."
"I...I understand."
"So as for Hyperworlds, the concept of dimensionality is transcended. However, the Drops predate all."
We appeared in another Drop without any disturbance of energy. This phenomenon left me puzzled.
"The core-like Nest"
He spoke, and I observed. The nest was stationed within the core with a gate that connects it to the surface world.
We moved without any disturbance again to the next Drop, whose Nest was visible in the Drop.
"Just as the Nest differs, the Hyperworlds structure is also different."
We were standing, but we kept leaping from one Drop to the other, observing their unique nature. I was growing frustrated, so I asked.
"What's this movement? I don't feel any disturbance in the energies, but we're reaching different locations with ease."
"Your body is moving unconsciously, syncing with mine to reach our next destination."
He raised his fingers and our clones? No, I felt my mind taking in different views at the same time.
"These aren't clones."
"Of course. It's us. We're everywhere in this system. Your body must've blocked your sights, but you'll adapt in time."
"'Same Laws that'll apply in the Hyperworlds,' you said."
I kept this information at the back of my mind, eager to find the answers. We're now in the space between Drops and a Drop appeared alongside another Drop. They shrunk until they became a ball-like size.
"This is my Drop. Prove you can create more worlds past my 'infinity'."
It wasn't a challenge, but he wanted to prove a point.
I took a hold of the Drop and began immediately.
To be continued...