ANSWERS: 3
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Probably not a building, in the sense you mean. We don't currently have strong enough materials to make a structure of "building" proportions that tall. We could theoretically build a construct into outer space, often discussed as a space elevator, which uses a very strong material called carbon nano-fibres for the elevator cable.
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You would need one helluva good engineering team. And it's hard to know when you've actually reached 'space' when you consider gravtiy and air, they technically reach even the moon... The building itself would have to be a good percentage of it's height and world's resources...which is alot. Also considering the change in climate...I doubt it would be possible with the resources we have now. No.
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Well, I too wonder if it would be possible. IT would seem to me that using carbon-nanotube based materials and a pyramid like shape it should be possible to build something tens of thousands of kilometers tall(it would require heavy automation, probably molecular manufacturing, for it to be cost feasible. ). I know if built in space such a structure would have no problems, but I'm not sure if the strength of the possible materials is enough to hold up against earth's gravity(with all the floors, cables, pipes, people, etc of a regular building). My guess is it would be, provided a pyramid like structure to distribute the weight.
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