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  "body": "\n## Summary\n\nA dynamic equation on a time scale is an equation that involves the delta derivative of an unknown function.\nThe function lives on a time scale $\\mathbb{T}$, a nonempty closed subset of $\\R$.\nIt is the basic object of [[time-scale calculus|30G1M35TK1]].\nOn $\\mathbb{T} = \\R$ it is an [[ordinary differential equation|0NT64JV96A]], and on $\\mathbb{T} = \\Z$ it is a [[recurrence relation|0FYX44GP92]], so one theory covers both cases at once.\n\n## Explanations\n\n### L1 human\n\nSome quantities change continuously, others change in steps, and some do both.\nA time scale is the set of times at which the quantity lives, for example all reals, all integers, or a union of intervals.\nA dynamic equation tells how the quantity changes from each time to the next one, using a derivative where time flows and a difference quotient across each gap.\nFor example, the equation $x^\\Delta = x$ with $x(0) = 1$ has the solution $e^t$ on $\\R$ but $2^t$ on $\\Z$, since on $\\Z$ it says $x(t + 1) - x(t) = x(t)$.\n",
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