Category:Parastrophes

This category contains results about Parastrophes.
Definitions specific to this category can be found in Definitions/Parastrophes.

$(1-3)$ Parastrophe

$\struct {S, *}$ is a $(1-3)$ parastrophe of $\struct {S, \circ}$ if and only if:

$\forall x_1, x_2, x_3 \in S: x_1 \circ x_2 = x_3 \iff x_3 * x_2 = x_1$

$(2-3)$ Parastrophe

$\struct {S, *}$ is a $(2-3)$ parastrophe of $\struct {S, \circ}$ if and only if:

$\forall x_1, x_2, x_3 \in S: x_1 \circ x_2 = x_3 \iff x_1 * x_3 = x_2$

$(1-2)$ Parastrophe

$\struct {S, *}$ is the opposite magma of $\struct {S, \circ}$ if and only if:

$\forall x_1, x_2, x_3 \in S: x_1 \circ x_2 = x_3 \iff x_2 * x_1 = x_3$