Interval Notation

a is finite?

include a?

a

-1

b is finite?

include b?

b

1

locale

American

European

IThe interval is

bounded and half-open.

In set notation, I =

{x | -1 < x ≤ 1}.

In interval notation, I =

(-1, 1].

A real interval is shown graphically and described in words, as a set, and in interval notation. (There is no interval notation for the empty set.) Here is a summary:

				American	European
○	open&closed	bounded	∅	—	—
●—●	closed	"	{x\|a≤x≤b}	[a,b]	[a,b]
●—○	half-open	"	{x\|a≤x<b}	[a,b)	[a,b[
○—●	half-open	"	{x\|a<x≤b}	(a,b]	]a,b]
○—○	open	"	{x\|a<x<b}	(a,b)	]a,b[
●⟶	closed	unbounded	{x\|a≤x}	[a,∞)	[a,∞[
○⟶	open	"	{x\|a<x}	(a,∞)	]a,∞[
⟵●	closed	"	{x\|x≤b}	(-∞,b]	]-∞,b]
⟵○	open	"	{x\|x<b}	(-∞,b)	]-∞,b[
⟷	open&closed	"		(-∞,∞)	]-∞,∞[