Xephyr's Meta-Equal Numbers Hypothesis

From KneeQuickie

The Meta-Equal Numbers Hypothesis states that there is a set of numbers which, when added to a number x, produce a sum equal to x; and for the operand ≠ 0. This means that for any real number, there are numerous different values of that number when adding the mutually inequal numbers from the set M, but which are all equal in the real set R. The Meta-Equal Unit may be defined as я.

Put in shorter terms, the Hypothesis states: "x + yя = x, for any x, any y, and я ≠ 0.", which necessites the following two formulas:
xя ≠ yя, for x ≠ y
xя = xя

The series of Meta-Equal Numbers begins thusly:

1 = 1 (1 = 1 + 0я)
1 = 1 + я
1 = 1 + 2я
1 = 1 + 3я

Unlike Infinitesimal Numbers, however, yя can never = 1, even for y = ∞.

Therefore, the end of the first series (excluding transfinites) is thus:

1 = 1 + (∞ - 3)я
1 = 1 + (∞ - 2)я
1 = 1 + (∞ - 1)я
1 = 1 + ∞я ≠ 2

To understand the meta-equal numbers one must discard one's notion of mathematic transitivity-- two numbers (e.g. 1+я and 1+2я) can be both equal to another number (e.g. 1), yet not be equal to each other.

It has been argued that, since they affect real numbers in the same manner as zero, therefore я = 0. This is especially suspicious in that since 1 = 1 + я, then 1 - 1 = 1 + я - 1, whence 0 = я. However, this can be seen to not be the case:

0x = 0y for any x, and any y
яx ≠ яy for x ≠ y

And the "proof" must be discarded by excluding the property of additive inverses, in much the same way as transfinites exclude the commutative property (∞ + 1 = w ≠ 1 + ∞).

"The Meta-Equal Numbers Hypothesis is the result of Xephyr sitting alone for hours on end thinking up random and weird shit that are brilliant and groundbreaking but have no conceivable practical application or absolute worth, and for this he should be commensurably recognized and rewarded." - Xephyr

(In situations where one cannot type я, the Meta-Equal Unit can also be written in using <&>)