asymptotically
Ever closer, never touching
Asymptotically describes approaching a limit or boundary without ever quite reaching it.
In mathematics, a curve may approach a line asymptotically, getting infinitely close but never touching.
The term extends to any gradual convergence: The algorithm's performance asymptotically approaches optimal.
In casual technical speech, it often just means eventually or in the limit: Asymptotically, it doesn't matter which method you choose.
Line touching curve once
- curveSmooth, angleless line
- functionPurpose or duty
- graphVisual data display
- limitMaximum allowed extent
derivative · integral · convergence · divergence · series · infinite series · Taylor · approximation
Coming toward something
infinitesimally · vanishingly · approximating · nearing · eventual · ultimately · threshold · boundary
State of balance
- steady stateUnchanging system condition
- stableSecure and unchanging
- unstableProne to sudden change
- attractorConvergence point for systems
basin · fixed point · orbit · trajectory · perturbation · damping · oscillation · decay
State of being complicated
- notationSystem of written symbols
- growth rateSpeed of increase
- running timeProgram's total duration
- algorithmFinite problem-solving procedure
efficiency · scaling · exponential · logarithmic · linear · quadratic · computational · bounds
tangent
Line touching curve once
limit · derivative · integral · convergence · divergence · series · infinite series · Taylor · approximation · behavior
approaching
Coming toward something
bound · infinitesimally · vanishingly · approximating · nearing · eventual · ultimately · threshold · boundary · endpoint
equilibrium
State of balance
- steady stateUnchanging system condition
- stableSecure and unchanging
- unstableProne to sudden change
attractor · basin · fixed point · orbit · trajectory · perturbation · damping · oscillation · decay · growth
complexity
State of being complicated
- notationSystem of written symbols
- growth rateSpeed of increase
- running timeProgram's total duration
algorithm · efficiency · scaling · exponential · logarithmic · linear · quadratic · computational · bounds · worst-case
asymptoticallyimmediately
Without any pause
instantly · directly · instantaneously · abruptly · suddenly
asymptoticallydivergently
In separating directions
explosively · exponentially · infinitely · without limit · chaotically