Closure notation help

Question

Example: Let <· be the relation on integers defined by x <· y if x + 1 = y.

• The transitive closure of <· is <.

• The reflexive and transitive closure of <· is ≤.

What do the dots mean next to the greater than and less than symbols?

Answer 1

Those dots are just what the writer of the problem chose to decorate the $<$ symbol with when defining his relation. They have no general meaning.