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Definition

Zeinyt (e) is held to be a lower bound on all Class _ Numbers. As such it is believed to lie below Class _, though it is unknown how far down it lies. *Θe is defined by the following 3 Axioms:

(A1) For every non-empty collection of objects, *Θe is either the unique least member of that collection, or there exists an object larger than *Θe that is smaller than every member of the collection.

(A2) *Θe is the only object with the unique property of being *signed. Being *signed is neither being positive, nor negative, nor any complex angle, nor signless, nor any other kind of sign (such as hyperpositive, hypernegative, etc.) other than itself.

(A3) Any number times a *signed object is automatically a *signed object.

Consequences

From it's definitions follow many consequences:

Firstly take the collection of all reciprocals. Either *Θe is in the collection or it is not. If it is, then it is the reciprocal of some fictional infinity. *Θe is the strictly least member of the set, which means it's reciprocal must be the largest possible fictional infinity. There is no largest fictional infinity however, therefore *Θe can not be in the set of all reciprocals. Therefore there must be a larger object than *Θe which is not the reciprocal of anything. It follows that *Θe can also not be the reciprocal of anything. Therefore:

1/*Θe is foundationally undefinable. Defining it leads to a violation of the TrueNoEnd Principle, which says there can not be a largest fictional infinity.

Furthermore *Θe must be smaller than any reciprocal of any fictional infinity. This implies that any fictional infinity or object times *Θe must be equal to no other object besides *Θe.

Because *Θe is *signed the product of *Θe with any other number must be *signed as well. Since it is unique in this sign, the product must be *Θe.

Furthermore

Э x *Θe = *Θe

Without contradiction to Э (Conkept). This is because this must be true of all numbers, so Conkept has smaller objects with this property, namely anything.

*Θe is believed to be remote. This means that for any interval (*Θe,x), there can be any fictional infinity number of objects strictly between them.

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