ε–N Visualizer for Sequences (xₙ)

See the band around L, place the cutoff N, and watch the points behave.

Controls

Sequence xₙ

Proposed limit L

ε (band half-width)

between 0.001 and 1

N (cutoff)

Number of points

more points = more detail

Show elements

ε-band N fence

ε-band limit line y = L x = N before N after N & inside band after N & outside band

Adjust L, ε, and N to test the definition.

Goal: for every ε > 0, find N so that for all n > N, |xₙ − L| < ε.

Tip: Try xₙ = n⁻¹, click Use known L, set ε small, then click Auto N(ε).