The world only has effectively infinite resources if growth slows down, because exponentials get out of hand surprisingly quickly.

For example at 1% energy growth per year it would only take around 9-10k years before to reach an annual consumption equal to all the energy in the Milky Way galaxy. By "all the energy" I don't just mean consuming all the solar energy from all the stars, and using all the fissionable material in reactors, and fusing everything that can fuse, and burning all the burnable stuff. No, I mean also using all the gravitational potential energy in the galaxy, and somehow turning everything that has mass into energy according to E=mc^2.

From there at 1% annual growth it is only another 2-3k years to using all the energy in the whole observable universe annually.

Population at 1% growth also gets out of hand surprisingly quickly. If we don't get FTL travel then in about 12k years we run out space. That's because in 12k years with no FTL we can only expand into a spherical region of space 12k lightyears in radius. At 1% annual growth from the current population in 12k years the volume of humans would be more than fits in the sphere--and that's assuming we can pack humans so there is no wasted space.

We actually have population growth under 1% now, down to around 0.85%, but that only gets us another 2-3k years.