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2. Tiny and miny - Wikipedia

   en.wikipedia.org/wiki/Tiny_and_miny

   In combinatorial game theory, a branch of mathematics studying two-player games of perfect information in extensive form, tiny and miny are operators that transform one game into another. When applied to a number (represented as a game according to the mathematics of surreal numbers ) they yield infinitesimal values.

3. Surreal number - Wikipedia

   en.wikipedia.org/wiki/Surreal_number

   All games are constructed according to this rule: Construction rule If L and R are two sets of games then { L | R} is a game. Addition, negation, and comparison are all defined the same way for both surreal numbers and games. Every surreal number is a game, but not all games are surreal numbers, e.g. the game { 0 | 0} is not a surreal number ...

4. Infinitesimal - Wikipedia

   en.wikipedia.org/wiki/Infinitesimal

   In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus , which originally referred to the " infinity - eth " item in a sequence .

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6. Increment theorem - Wikipedia

   en.wikipedia.org/wiki/Increment_theorem

   In nonstandard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then Δ y = f ′ ( x ) Δ x + ε Δ x {\displaystyle \Delta y=f'(x)\,\Delta x+\varepsilon \,\Delta x} for some infinitesimal ε , where Δ y = f ( x + Δ x ) − f ( x ...

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