What is an open interval?

Question

Isaiah Anthony · Accepted Answer

undefined An open interval is a set of real numbers between two specified values, where the endpoints are not included in the interval. It is denoted by (a, b), where a and b are the two values defining the interval.

Hazel Anglin · Answer

See explanation...

If #a# and #b# are Real numbers with #a < b# then #(a, b)# is used to denote the numbers which lie strictly between #a# and #b#. This is called "the open interval #a#, #b#". In symbols we could write: #(a, b) = { x in RR : a < x < b }# This reads #(a, b)# is the set of elements #x# in the set of Real numbers (#RR# for short) such that #a < x# and #x < b#. When we want to talk about all the Real numbers we may write: #(-oo, +oo)# The symbols #-oo# (minus infinity) and #+oo# (plus infinity) are not really numbers. You can picture them as being at the extreme left and right ends of the Real number line. Any Real number #x# satisfies: #-oo < x < +oo# If we want to talk about any number greater than #5#, we can write: #x in (5, +oo) " "# (#x# is in the open interval "#5# to plus infinity") If we want to talk about any number less than #5#, we can write: #x in (-oo, 5) " "# (#x# is in the open interval "minus infinity to #5#") If #z != 5# then either #z < 5# so #z in (-oo, 5)# or #z > 5# so #x in (5, oo)#. The amalgamation of these two sets is called the union and is denoted: #(-oo, 5) uu (5, +oo)#

Ethan Adkins · Answer

undefined An open interval in mathematics is a range of real numbers that does not include its endpoints. It is denoted by parentheses, such as $ (a, b) $, where $ a $ and $ b $ are the endpoints of the interval. The numbers between $ a $ and $ b $, excluding $ a $ and $ b $ themselves, are considered part of the open interval.