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It is in the conceptualization of the actual construction of a dyson sphere that the problems that contain it to science fiction begin to emerge.
In order to build a structure the amount of material required would be beyond anything we could mine from a single planet. All of the inner planets could be used without completing the sphere. Thought has been put forth however about mining the asteroid belt, but that venture on its own would prove quite challenging.
Even if the proper ammount of material could in fact be gathered, the fact is that at least with our current knowledge there is no known material that could withstand the stresses required of a dyson sphere, particularlly because it would have to be maintained in a proper position such as to have every part of the same distance from the star at the center. Any part that came closer would be pulled on harder and the whole sphere would be torn apart by gravity. Also in order to make the sphere livable it would need to spin in order to provide a simulation of gravity through centripetal acceleration, and any sort of spinning would place even further stress on the structure.