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DonPunch, that's an overly precise definition of finite in the current context. We have semi-finite resources, finite resources and renewable resources. There's no point in getting into things like photosynthesis meaning resources are infinite because humans could quite easily wipe out the entirety of plant life within a century or so. However, more importantly, any mass changing processes are nothing more than energy transfers - the same amount of energy is still present. In this definition of finite, the Earth's volume is constrained and cannot be altered easily. Merely changed.
Furthermore, these changes in mass are truly miniscule - you'd have to eject mass at something like 11.2k/s to escape the atmosphere alone, and that doesn't happen often or easily. But this is an argument that could go on forever and technically you could work with many definitions and be correct either way.
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Stormy, actually, asteroids do hold a massive amount of resources - they're partly responsible for things like silicon, gold, rubidium deposits and so on[
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3]. The problem with resource capturing asteroid projects is that they cost far, far more than what you'd get out of them. That applies to things on Earth as well - we don't go for the materials in the mantle because getting there just wouldn't be worth it at the current time.
To quote Wikipedia, which sums up the figures quite well because I can't be arsed to double check everything it says:
In 1997 it was speculated that a relatively small metallic asteroid with a diameter of 1.6 km (0.99 mi) contains more than $ 20 trillion USD worth of industrial and precious metals. A comparatively small M-type asteroid with a mean diameter of 1 kilometre (0.62 mi) could contain more than two billion metric tons of iron–nickel ore, or two to three times the annual production of 2004. The asteroid 16 Psyche is believed to contain 1.7×1019 kg of nickel–iron, which could supply the world production requirement for several million years. A small portion of the extracted material would also be precious metals.http://en.wikipedia.org/wiki/Asteroid_mining