2 edits
symmetry on an operation R over Z is defined thus,
xRy => yRx
e.g. if x=y then y=x, if 3|(x-y) then 3|(y-x)
anti-symmetry on R over Z is defined thus,
if xRy and yRx then x=y,
e.g. x(< =)y and y(< =)x then x=y (< = is less than or equal to)
Question: is the operation ' < ' symmetric, anti symmetric, neither or both?
Originally posted by geniusMaybe relation is more appropriate than operation.
symmetry on an operation R over Z is defined thus,
xRy => yRx
e.g. if x=y then y=x, if 3|(x-y) then 3|(y-x)
anti-symmetry on R over Z is defined thus,
if xRy and yRx then x=y,
e.g. x(< =)y and y(< =)x then x=y (< = is less than or equal to)
Question: is the operation ' < ' symmetric, anti symmetric, neither or both?
Depends what meaning you impose on that symbol > but if we assume the default it is neither symmetric, nor anti-symmetric.
2 edits
Originally posted by ilywrinnot sure, but it seems like it is anti-symmetric to me, because a>b and b>a cannot happen both, and therefore the statement: if a>b and b>a , then a=b is true
Maybe relation is more appropriate than operation.
Depends what meaning you impose on that symbol > but if we assume the default it is neither symmetric, nor anti-symmetric.
Originally posted by aginisno no, antisymmetric really is this by definition: if xRy and yRx, then x=y.
you're discussing relations and antisymetric is if xRY then NOT yRx as a relation can be either reflexive (for all x xRx) or anti-reflexive (for all x NOT xRx)
It is not the opposite of symmetric
Originally posted by Skinn13wooops righ you are ...look what a good nights sleep will do 😳
no no, antisymmetric really is this by definition: if xRy and yRx, then x=y.
It is not the opposite of symmetric
(xRy ^ yRx)-> x=y looks more familiar. I was thinking antisymmetric AND antireflexive shame on me.