border on vs converge

border on and converge both are verbs.

Word	Noun	Adjective	Verb	Adverb
border on	No	No	Yes	No
converge	No	No	Yes	No

As verbs, converge is a hyponym of border on; that is, converge is a word with a more specific, narrower meaning than border on:

border on: come near or verge on, resemble, come nearer in quality, or character
converge: approach a limit as the number of terms increases without limit

border on (verb)	converge (verb)
come near or verge on, resemble, come nearer in quality, or character	come together so as to form a single product
	move or draw together at a certain location
	be adjacent or come together
	approach a limit as the number of terms increases without limit