I want you to think about, for a minute, the notion that you can have a number bigger than all of the atoms in the universe :-). From that, you can see that its possible to have more 'dollars' than there are atoms in the universe. Specifically, without defining 'growth' you can't reason about the limits on that growth.

The other point that simplified analysis fails to consider is that you are inside the system so as it "grows", it also "changes". If you lived in the 70's with the tales of how we're going to run out of fossil fuels by 2000, looking back you can see how things changed (cars got more efficient, other sources were discovered, etc).

My macroeconomics professor had a funny saying that you could take any segment of a sinusoid and use that to extrapolate forward and get the wrong answer about what the waveform was going to do. In my differential equations class we got to see how you could predict some things if you new both the initial conditions and you continued to refine your model. But to predict all things your model needed to take into account all variables and their impact, and it was the unknown variable problem that messed up predictions using that method.

As long as you calculate inflation “correctly”, you can have infinite growth lol. It will be fake but you know, line goes up.

That implies that economic activity is confined to this planet. Even today we can see this doesn't hold true as we already have activity in orbit. Also, economic activity is less and less tied to physical constraints as technology progresses and digitization spreads.

If I sell you a banana for $1, and you sell it back to me for $1, we have just created $2 of GDP. The trick is we need to repeat this process faster and faster over time. Luckily computers also get faster every year due to Moore’s law, so growth shouldn’t be an issue.

In fact, every person in the country could take turns with the banana for a brief period of time (provided they quickly sell it to the next person) which should enable broad prosperity for all.

Let me introduction you to asymptotes.

Come on, don't be pedantic. We are so far from hitting any limits on growth imposed by a finite planet as to be effectively unlimited.