- 12 Oct '06 10:22 / 2 editssymmetry 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? - 12 Oct '06 17:41

Maybe relation is more appropriate than operation.*Originally posted by genius***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. - 12 Oct '06 18:30 / 2 edits

not 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*Originally posted by ilywrin***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. - 12 Oct '06 22:36

no no, antisymmetric really is this by definition: if xRy and yRx, then x=y.*Originally posted by aginis***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 - 13 Oct '06 09:17

wooops righ you are ...look what a good nights sleep will do*Originally posted by Skinn13***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. - 13 Oct '06 15:02

yes-i meant relation not operation*Originally posted by Skinn13***not 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**

i think you've got it, but could you give a better explanation?