This sequences and limits explorer visualizes the concept of infinity for high-school Math I sequence units, Math II introductions to limits, continuity, and differentiation, and undergraduate calculus and real analysis courses covering the formal ε-δ definition of limits. Adjust the first term and common difference/ratio of arithmetic (constant additive increment d), geometric (multiplicative ratio r), and harmonic (reciprocals forming an arithmetic sequence) progressions, then observe the numeric progression of terms a₁ through a₂₀ in real time, watching whether the sequence converges to a target value or diverges as n grows infinitely. The convergence of a geometric sequence hinges decisively on the common ratio r: |r| < 1 converges to 0, r = 1 converges to the first term, and r > 1 or r ≤ −1 diverges. Contrary to the common misconception that 'the limit means reaching infinity', a limit is not an arrival—it describes the property of a sequence's terms approaching a target value with arbitrarily small error as n grows without bound. This is the foundational concept underlying all of calculus and analysis.