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Definitions:
Noun
asymptote
Definition: a straight line that is the limiting value of a curve; can be considered as tangent at infinity; "the asymptote of the curve"
Definition: A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity".
Verb
Definition: To approach, but never quite touch, a straight line, as something goes to infinity.