Mastroids

The class L ( M ) {\displaystyle {\mathcal {L}}(M)} of all flats, partially ordered by set inclusion, forms a matroid lattice . Conversely, every matroid lattice L {\displaystyle L} forms a matroid over its set E {\displaystyle E} of atoms under the following closure operator: for a set S {\displaystyle S} of atoms with join ⋁ S {\displaystyle \bigvee S} ,

In math the same kind of transplantation occurs all the time. In his widely cited 1994 essay “ On Proof and Progress in Mathematics ,” the influential mathematician William Thurston explained that there are dozens of different ways to think of the concept of the “derivative.” One is the way you learn it in calculus — the derivative as a measure of infinitesimal change in a function. But the derivative appears in other guises: as the slope of a line tangent to the graph of a function, or as the instantaneous speed given by a function at a specific time. “This is a list of different ways of thinking about or conceiving of the derivative, rather than a list of different logical definitions ,” Thurston wrote.

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