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Binary is suitable for describing discrete systems, corresponding to logic.
Decimal is suitable for describing continuous systems, corresponding to functions.

Binary → Discrete system → Corresponds to formal logic
Decimal → Continuous system → Corresponds to analytic functions

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I. Binary

1. Essential properties

· Only two discrete states, 0 and 1; discontinuous, no interpolation, no intermediate transition.
· Naturally suited for: presence/absence, truth/falsehood, on/off, existence/non-existence, yes/no.

2. Corresponding levels

· Mathematics: discrete mathematics, set theory, Boolean algebra, mathematical logic.
· Physics: discrete events, quantum state discreteness, countable particles, number of origins.
· Thinking: judgment, proposition, reasoning, causal logic.

3. One-sentence characterization

Binary is the language of existential logic, suitable for describing discrete structures, boundaries, and yes/no dichotomies.

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II. Decimal: Naturally coupled with "continuity + functions"

1. Essential properties

· Ten progressive steps from 0 to 9, capable of infinite subdivision, interpolation, and smooth transition.
· Naturally suited for: flux, gradual change, curves, smooth fields, continuous quantities.

2. Corresponding levels

· Mathematics: calculus, analytic functions, differential equations, manifolds, continuous curvature.
· Physics: gravitational fields, spacetime continuity, velocity and acceleration, smooth trajectories.
· Thinking: rates of change, trends, evolution, continuous quantitative variation.

3. One-sentence characterization

Decimal is the language of continuous evolution, suitable for describing flux, smoothness, and functional mappings.

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