I don’t know sheaves (except that they are a generalization of differential geometry or something?), but a great example of local to global is the fundamental theorem of calculus.
You take this property of a function that’s only defined in an arbitrarily small neighborhood of a point, and from it you can determine the function’s value anywhere else. That is, you take infinitesimally small changes (e.g. velocity) and add them up in the right way and get finite changes (e.g. distance).
It’s more interesting than it sounds because you aren’t computing a sum or something with numbers when you add up infinitesimal change. Local/infinitesimal change is in some ways a different beast than finite/global change.
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I don’t know sheaves (except that they are a generalization of differential geometry or something?), but a great example of local to global is the fundamental theorem of calculus.
You take this property of a function that’s only defined in an arbitrarily small neighborhood of a point, and from it you can determine the function’s value anywhere else. That is, you take infinitesimally small changes (e.g. velocity) and add them up in the right way and get finite changes (e.g. distance).
It’s more interesting than it sounds because you aren’t computing a sum or something with numbers when you add up infinitesimal change. Local/infinitesimal change is in some ways a different beast than finite/global change.