SPOILER Nameless Anomaly Gear Analysis…

So, as we all know, TNA rewards 6 accessories (Simulacrum, Detachment, Collection, Ingress, Forbearance, Breakthrough) and the Boundless Set (Aleph Null, Nonexistence, Continuum, Divergence, Fractal, Infinitesimal, Recursion).

I believe like those kinda tie in with the raid's events…?

So from a canon perspective, TNA is practically down-right impossible to happen, by which I mean that the player character is the ONLY normal person (excluding them pesky NPCs) who has survived the silent expanse (and probably the only person who knows about it too).

So purely from a gameplay process perspective with deeper lore, the accessories basically form an extremely abridged narrative of the raid. You start with Forbearance for what is to come, then execute a Detachment from reality, creating a Simulacrum of yourself in the transition, Breaking through the barrier between the realms of influence, and finally starting an ingress into the Archipelago; Fighting a collection of warped, dernic enemies as you go through.

The boundless set references the multiple aspects of the Nameless and the entire Archipelago itself (I don't know what Aleph Null means though). Nonexistence is pretty easy to gauge, it's basically the state of reality itself in the raid. Divergence would probably refer to void holes connecting to dimensions diverging from Wynn's reality; Fractal is a reference to the bizarre creatures from the Archipelago; Continuum would be referring to the fact that many mobs from the raid correspond to creatures in Wynn's reality (Such as the Glow Bug to Nivla Spiders, and Dernapiens to humans), essentially a continuum of life; Infinitesimal would probably could be a statement referring to:
1. the infinite War of the Realms (rawr of the wealms)
2. the infinitely large expanse of the void
3. the infinite annoyingness of greg's skulls
And recursion would probably be more… meta? Lore-wise, defeating the nameless once is enough… more than enough. But players kill it, once and again, and it just revives, and the raid just begins anew. A recursion of events and spacetime to be descriptive.

thank you for reading my speculating ^

 

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It's the concept that some infinities can be larger than others. For example, all whole, positive numbers is an infinite set, but all whole numbers should therefore be a larger infinite set, despite the fact they're both infinite. Aleph-Null (or Aleph-0) is the idea of the "smallest infinity".

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All of the boundless set is tied to the ideas of infinity.
Infinitesimal - infinitely small
Fractal - infinitely repeating pattern
Aleph-Null - smallest form of infinity
Continuum - stretching on forever
Recursion - infinite repetition
Divergence - mathematical concept of a sequence diverging onward to positive or negative infinity
Nonexistence - nebulous idea of infinite nothing

Even the word Boundless itself, meaning "unlimited"

 

you lost me at the math

 

here's what i use to explain not all infinities are equal (though deus is correct, and number groupings is a great example):
the number of different decimal values between 1 and 2 is infinite
but the number of different decimal values between 1 and 3 is an even bigger infinity
infinity is only a kinda number, so trying to explain anything involving is kinda wacky

(deus's example, in other words, is that there are an infinite number of positive numbers, but including every other number is even more infinite)

 

They are the same infinity since you can do a 1-1 mapping (double and subtract 1), an example of different sized infinities are the reals between 0 and 1 and the rationals between 0 and 1

 

But one of them has more in it, and thus why Aleph exists in math

 

We say that two sets have the same size if there exists a bijection between their elements (as point_line already said), that is, for every element in one of the sets, you can pair that up with one and only one element from the other set.
Here is a very simple example of this:

Here the set containing the elements {1, 2, 3, 4} has the same size as the set with the elements {A, B, C, D} because you can do the pairing process I described earlier.

This definition of "same size" can be extended to infinite sets as well. This is why the set containing all the positive whole numbers have the same size as the set containing all the whole numbers: I can find a bijection between the two.

Let's take our second set with the elements {..., -2, -1, 0, 1, 2, 3, ...}. Now I'm going to order this set like this: {0, 1, -1, 2, -2, 3, -3, ...}. Now I can take our second set, {1, 2, 3, 4, ...}, and simply pair the elements in this order: I pair 0 with 1, 1 with 2, -1 with 3 and so on (this is not a full proof but I'm fairly certain it is correct).

(Now I know that the fact that these two sets have the same size may seem counterintuitive, but going off of the definition gives us this result so we have to roll with it.)

It can also be shown that both the set of all the whole numbers and the set of positive whole numbers have the same size as the natural numbers ({0, 1, 2, 3, ...}). We say that a set has size (the rigorous term would be cardinality) aleph-null (ℵ_0) if there exists a bijection between it and the natural numbers. Sets with cardinality aleph-null are what we call countably infinite sets.

What doesn't have the same size as the natural numbers is the set of all real numbers between 0 and 1, or the set of all real numbers. It can be shown that you can't pair up the natural numbers with the real numbers between 0 and 1: there are always going to be real numbers left out. For a simple but effective proof, look up Cantor's diagonal argument.

Now this is how far my "expertise" goes, so I'm going to stop here.

While I'm here though...

Those two have the same cardinality.
Take this function: f: [1,2]->[1,3]; f(x) = 2x-1.
This pairs every number between 1 and 2 exactly to one number between 1 and 3.

A sequence is divergent if it isn't convergent. For example, the sequence {1, -1, 1, -1, ...} is divergent even though it doesn't blow up to positive or negative infinity. (But it is correct that a sequence going to either positive or negative infinity is divergent.)

Spoiler: Um ackchyually

☝️☝️☝️

Spoiler: rip

the forums can't render the nerd emoji

 

when did this turn into a calculus discussion post