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This will almost certainly not happen ever. Or anytime in the next century anyways.
The thing is, even if you could build an elevator that high, it is not like once you were in space you could just put on a space suit and start floating away or build spaceships with materials you got up there.
The reason that astronauts experience zero G has nothing to do with being in space of being 'so far' away from the earth. the reason is because they are essentially in a constant state of falling, but are moving so fast that they continually fall over the horizon and appear to be 'floating' above the earth. If they were to come to a complete stop, they would immediately plummet back to earth.
In other words, you don't just need to build a giant elevator, you also need to accelerate to a great speed once you get up there. And if you are just using the elevator to get materials into space, you need to figure out a way for astronauts to pick it up while flying past at thousands of miles per hour.
So there is really no point even if you could build it.
A better question would be, how long till we have a functioning mass driver for which to propel objects into space. That or some other device which allows us to get an object into space whereby the fuel is not a part of the payload.
Regards
Brad S
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do some reaserch before making retarded claims buddy. The space elevator would actually be in geosynchronous Orbit w/ the earth.
Geo-synch-ron-ous o-r-b-i-t. sound it out.