asymptote

Forever-approaching line

An asymptote is a line that a curve approaches but never quite reaches, getting infinitely close without touching.

In mathematics, functions may have horizontal, vertical, or oblique asymptotes that describe their behavior at extreme values: The graph approaches the x-axis asymptotically.

Figuratively, an asymptote suggests a limit that can be approached but never attained: Perfection is an asymptote.

calculus

limit

Maximum allowed extent

derivative · differential · integration · epsilon · delta · continuity · sequence · series · behavior · tend

curve

hyperbola

Curve with two branches

coordinate · horizontal · vertical · oblique · slant · line · exponential · logarithmic · rational · polynomial

limit

convergence

Process of approaching sameness

unreachable · approximation · bound · ceiling · floor · saturation · plateau · cap · maximum · minimum

behavior

growth

Increase in size

stabilization · equilibrium · steady-state · saturation · plateau · tapering · flattening

Categories
Opposites
curve-line relationship

asymptoteintersection

Point where paths meet

crossing point · intercept · secant · crossing · meeting point

limit behavior

asymptoteconvergence point

Where separate paths unite

attainment · arrival · terminus · endpoint

convergence behavior

asymptotedivergence

Separation from common origin

intersection · discontinuity · inflection point · vertex · origin

Family

asymptotic, asymptotically, asymptotes

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