[tomjen3]

You seem to be under the assumption that the population is going to grow towards infinity. The UN projects that we will stay under 10 billion (http://en.wikipedia.org/wiki/Projections_of_population_growt...) and even the highest only have us at 16 billion at the end of this century (compare that to the growth in the 20th century).

So unless there is a relatively low limit for total humans on this planet, we won't reach it before we become a spacefaring race, at which point the limit will be the carrying capacity of the Universe.

[onnoonno]

> So unless there is a relatively low limit for total humans on this planet, we won't reach it before we become a spacefaring race, at which point the limit will be the carrying capacity of the Universe.

But even in that case, you can only have at most polynomial growth (human habitat spherically expanding with speed of light) instead of an exponential one.