It's not clear to me why this relation is not total:
$\{(x,y)|x=y\}$
The way I interpret this is, since x = y, it is always true that (x,y) or (y,x) is part of the relation. Doesn't this imply that the relation is total?
Asked
Active
Viewed 73 times
-1
-
What is the definition of total? – Tim Raczkowski Jan 01 '17 at 17:31
-
Either (x,y) or (y,x) has to be part of the relation, for all vertices x and y – user403371 Jan 01 '17 at 17:33
1 Answers
2
This is not true. Suppose $x=2$ and $y=3$. Neither $(2,3)$ nor $(3,2)$ are members of the relation.
Tim Raczkowski
- 20,046
-
But x has to be equal to y in order for the tuple to be part of the relation, doesn't it? – user403371 Jan 01 '17 at 17:53
-
Yes, that's correct. Looks like you're reasoning is circular. Your argument seems to be the following: If $(x,y)$ is in the relation, then $x=y$ which means that $(x,y)$ is in the relation. But you assume $(x,y)$ was in the relationship to begin with. – Tim Raczkowski Jan 01 '17 at 17:57