Had some trouble with this question in an exam recently, and wanted to make sure I reasoned correctly. The question was:
$X$ is a set of pairs of real numbers $(x,y)$, with absolute values less than or equal to $10$.
$R$ is an order relation on $X$ defined as $$ R=\lbrace \space (x,y), (x',y') \in X \times X \space |\space x \leq x' \wedge y \leq y' \space \rbrace $$ with $\leq$ the usual order on the reals.
Find the meet (greatest lower bound) and join (greatest upper bound) of the subset $A$, where $$ A=\lbrace \space (x,y) \in X \times X \space | \space (x-1)^2 + (y-2)^2 = 100 \space \rbrace $$
Now am I right in saying that while there are a number of pairs $(x,y)$ that will satisfy $A$, these are not necessarily comprable and that therefore no glb or lub exists for $A$?