limitsand
Limitsand is a fictional term used in theoretical discourse to describe a framework that combines asymptotic limits with bounded resource constraints. The term is a portmanteau of "limit" and "sand" intended to evoke a sandbox-like setting where convergence is studied under finite resources. In this framework, one considers a sequence (or net) {x_n} in a metric space (X, d) together with a bound function b(n) ≥ 0, and requires that x_n converges to some x ∈ X with d(x_n, x) ≤ b(n) for all n, with b(n) → 0 as n → ∞. The difference from standard convergence is the explicit tracking of resource-related bounds that may influence the choice of approximants or the pace of convergence.
Origins and context: Limitsand appears in educational or speculative settings to illustrate how convergence interacts with
Applications and relation: While not part of formal mathematical theory, the notion helps discuss strategies for
See also: limit, convergence, rate of convergence, bound, bounded rationality, sandpile model.