Use a bracket to indicate that the endpoint is included in the interval a parenthesis to indicate that it is not.
Brackets are like inequalities that say or equal
parentheses are like strict inequalities.
##(37)## includes ##3.1## and ##3.007## and ##3.00000000002## but it does not include ##3##. It also includes numbers greater than ##3## but it does not include 7.
People sometimes say this is ##3## to ##7## exclusive (Excluding the endpoints)
##[4 9]## includes ##4## and every number from ##4## up to ##9## and it also includes ##9##
People sometimes say this is ##4## to ##9## inclusive (Including the endpoints)
##(ab) = {x : a< x and x< b}## ##[ab] = {x : a<= x and x<= b}## Of course mixed intervals ##(ab]## or ##[ab)## are also possible. The symbols ##-oo## (and ##oo##) are used to indicate that there is no left (right) endpoint for the interval. They are not endpoints but indicators that there is no endpoint. They always take parentheses. Quick examples: Domain of ##f(x)=sqrtx## is ##[0 oo)## Domain of ##g(x)=1/sqrtx## is ##(0 oo)##