Operative Transforms
 

1. The Formulae of the Universe

IAO (iota, alpha, omega) was the Greek form of the Tetragrammaton, IHVH (Yod-He-Vau-He, or Jehova, the “Bringer of Light”), the Hebrew divine name for God. Although a reference to Jahova (or Yahweh), IAO was also widely associated with both Hermes and Bacchus (Iacchus), especially in ancient magical texts and amulets.
As a Gnostic god form, IAO is both a sun-god and mystery-god.

- Free Encyclopedia of Thelema

The Supernal Triad - It should be noted that the primordial Trinity of Father-Mother-Son is in fact a gloss of a deeper formula, which is Father – Mother – Son –Daughter. This is expressed clearly in the related forms of IAO and YHVH. The relationship between them may be written as IAO == YHVH, with IAO (81) and YHVH (26), the sum of which, 107 = 1+0+7=8. IAO is 8+1=9 and Y (or I ) HVH is 2+6=8 and the form holds as 9+8=17 and 1+7=8. The IAO formula is more perfect theosophically as it expresses the form in fewer terms but the formula of YHVH expresses a deeper mystery in that the second letter, Heh, represents the Mother, the Unborn or Thought of the Bythos, Depth or Father and the fourth letter, Heh again, represents the Daughter but with the same letter as the Mother. Now the meaning of this should be clear; the Son is a Hypostasis of the Father, but has come into being via the Mother or the First, whereas the Daughter being an extension of the Mother has no intermediate form, that is, She (Babalon-Hekate) IS THE MOTHER projected into the Universe, whereas the Son is the SUBSTANCE of the Father MANIFESTED (the Father or Bythos is Himself the Uncreate or Eternal Unmanifested Potential) and thus reveals the perfectly the Alchemical formula of the Universe.

It hardly needs to be mentioned that the misunderstanding of this relationship has caused much error due to the attempt by various schools of philosophy to force one or the other of the formulae to be the foundation of a theological structure, which of course can never achieve stability if it takes into account only one half of the formula.

Now the form balances as YHVH = IAO which is
[81 =26] or [(81-26) == (26-26)
which gives [55 , (5+5) = 10] == 0
{1+0=} +-1 == 0.

2. The Hermetic Axiom in the New AEON

Every number is infinite; there is no difference.
-Liber Al vel Legis I 1:4

For that which is above is that which is below and that which is below is thus that which is above, one substance, one being in the divisions of time and space.
- The Book of Transmutations

…representing the formula of cyclic return by the equation 0-2; that is, 0= (+ 1)+ (-1). This formula is represented biologically by the congress of the sexes. The positive element of the equation is Will (Thelema), dynamic, masculine; the negative element is Love (Agape), passive, feminine. Their union is the basis of the magical ecstasy that polarizes the active and passive components of existence, reducing them to Zero. From that Void (Naught or Nuit) a new creation emerges, ready to begin the process again.
- Grant, Kenneth The Magical Revival

In Crowley’s Cult she is Nuit, of whom 0=2 is the mystical formula
- Grant, Kenneth The Magical Revival

One meaning of the 0=2 formula is that everything is made of Nothing or manifests spontaneously from Nuit. In a vacuum, pairs of particles, matter and anti-matter, are continuously being created out of nothing only to come together again in annihilation. As Aleister Crowley elaborated on the 0=2 formula, 0=(+1) + (-1).
- Free Encyclopedia of Thelema

Thus the formula, 0==+-1 is equivalent to 0==2 ( or abstractly, 0==(+-x) since any number produces the same result. ) which signifies the identity of the (totality of the) Universe with the infinite.