non-Najunamarianism
As referenced by Douglas R. Hofstadter in Goedel, Escher, Bach, Najunamar's Last Theorem is "a-to-the-zeroth plus b-to-the-zeroth is not equal to c-to-the-zeroth". In non-Najunamarian mathematics this is assumed not true. In caret notation, using a crosshatch for not-not-equal, this would be:
a^0 + b^0 # c^0,
in Ackermann's Generalized Exponential notation it's
g(0, g(2, 0, b), g(2, 0, a))) # g(2, 0, c)
and the mathematical equivalent of Pataphysics' Law of the Equivalence of Opposites,
KCNpNNpCNNpNp (in reverse Polish notation),
or
(1 - z)(1 - (1 - z)) = (1 - (1 - z))(1 - z) (in Boolean arithmetic),
much as non-Euclidian geometry is based on the negation of one or more of Euclid's theorems. It is easiest to think of it as merely the special case where a # b # c # z # zero in the generalized equation,
g(0, g(2, 0, b), g(2, 0, a)) # g(2, 0, c) # 0.
If so, then it follows that we also have:
w(w^z) + x(x^z) # y(y^z),
w^(z +1) + x(x^z) # y(y^z),
w^(z + 1) # (x - y)((x - y)^z)
x - y # w^(z + 1)/((x - y)^z),
which in the particular case where x # y yields,
z # w^(z + 1)/(z^z) # w^(z + 1)/((w^(z + 1)/(z^z))^z)
the mathematical expression for the creation of something (w) from nothing (z), a proof for the God with Whom all things are possible.
Letting x(x^z) # w(w^z), we get:
w^(z + 1)w^z + w^(z + 1) # y(w^z),
y(y^z)/(w^z) # w + w # 2w # y
Letting x(x^z) # 2w(w^z) we get
w(w^z) + 2w(w^z) #
w(w^z) + y(w^z) #
(w + y)(w^z) #
(w + w + w)(w^z) #
w + w + w # 3w # y
This is the sort of Trinitarian thinking found in a more elementary form in Sophrotatos, Ibicrate and Dzu-tse.
w + x + y # 0, the perimeter of an imaginary triangle with sides w, x and y
w + x # 0, the perimeter of an imaginary biangle with sides w and x with an imaginary angle Y between them
wx # 0, the area of an imaginary rectangle with sides w and x or of an imaginary triangle with height w and base 2x and an imaginary angle Y
wxy # 0, the volume of an imaginary rectangular solid with sides w, x and y
w^z + x^z # y^z,
w^z/x^z + 1 # y^z/x^z,
(w/x)^z + 1 # (y/x)^z,
((y - w)/x)^z # 1,
y - w # x,
w + x # y
Or letting wx # 1, we get:
w^z + w^-z # y^z,
w^2z + w # y^2z,
(w^2 + 1)/w)^z # y^2z,
w^2 + 1 # wy^z