(Note: Please do not take this as actual maths, I just came up with this and thought it was cool)
First, we shall declare that all real numbers form a circle, with 0 at the bottom, CAI / Ω at the top, Infinity (ℵ0) on the right, and Negative infinity on the left. However, we shall use σ (lowercase sigma) as Negative infinity instead of -∞.
ʃ[]
THE FIRST SET - ʃ
ʃ is the symbol used to symbolise this entire set, it is also equal to:
- n
÷0, n · Ω ∞-∞, σ - σ
ε is sort of the 'midpoint' between 0 and ∞, same goes for δ but with 0 and σ
THE SECOND SET - ɼ
0 and Ω are considered 'absolute numbers', and ∞ and σ are classified as 'infinite numbers' (unsurprisingly)
ɼ[]
We can go beyond ʃ, the symbol for this, new, weird set is called 'ɼ',
Its 'version' of 1 is Vsaue aka 'Λ'
Now obviously, we can continue with this, getting bigger and bigger sets,
The ƒractal nature of numbers[]
Here is a list of the first eleven sets:
Set 0: ∅ "Nul"
Set 1: ʃ "San"
Set 2: ɼ "Ret"
Set 3: ɭ "Luth"
Set 4: ʈ "Top"
Set 5: ȴ "Ler"
Set 6: ʝ "Hok"
Set 7: ȶ "Thyo"
Set 8: ʆ "Shop"
Set 9: ʄ "Zun"
Set 10: ʃ∅ "San-Nul"
Set 11: ʃʃ "San-San"
As you can see, this is in a base 10 system, and is just going to be another longer number line, we can turn this into another circle. Set Vsaue is the version of 1 in this set.
THE METASET - ʃ₂
This is the 'The metaset',
we can then do the same thing with this to get ɼ₂ and so on,
eventually we will get the set: ʃ₃,
Going on and on and on with this forever we will eventually get ʃ∞, but that's not the end, we can do this for every other number, beyond infinity.
But no matter how much you do this, you will never reach the inaccessible number beyond all this... ƒ.
(Note: 'ƒ' is pronounced "Ful")