Etymology
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asymptote (n.)

"straight line continually approaching but never meeting a curve," 1650s, from Greek asymptotos "not falling together," from a- "not" (see a- (3)) + assimilated form of syn "with" (see syn-) + ptotos "fallen," verbal adjective from piptein "to fall," from PIE root *pet- "to rush; to fly." Related: Asymptosy.

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Definitions of asymptote

asymptote (n.)
a straight line that is the limiting value of a curve; can be considered as tangent at infinity;
the asymptote of the curve
From wordnet.princeton.edu