lower bound vs boundary

lower bound and boundary both are nouns.

Word	Noun	Adjective	Verb	Adverb
lower bound	Yes	No	No	No
boundary	Yes	No	No	No

As nouns, boundary is a hypernym of lower bound; that is, boundary is a word with a broader meaning than lower bound:

lower bound: (mathematics) a number equal to or less than any other number in a given set
boundary: a line determining the limits of an area

Other hypernyms of lower bound include bound, edge.

lower bound (noun)	boundary (noun)
(mathematics) a number equal to or less than any other number in a given set	the greatest possible degree of something
	the line or plane indicating the limit or extent of something
	a line determining the limits of an area