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Is it possible to divide it indefinitely into smaller and smaller units?
possible
Yes
But it requires work/development. I think the community would easily handle the upgrade.
In that case, could we have virtually infinite supply?
No.
If you have a pizza, and you keep cutting it into more slices, you don't have infinite supply of pizza.
A pizza is a static physical object that, if divided too much, becomes so small that it loses its "function" and can't be shared among people.
Bitcoin, on the other hand, can grow in value and, if divided, the smaller units can still be as useful as the bigger ones.
We could reach a point where we Bitcoin keeps growing in value and we keep dividing, creating a virtual infinite supply.
I say virtual because the max number of BTC will always be the same, but the division of it creates valuable units that retain their original function.
Sounds like you've thought this through. I'm sticking with my answer. Good luck to you.
The absolute number of bitcoin in supply isn't important for its usability as money. The idea that value of each unit increases as supply is lost is equivalent to the maintaining of equilibrium. The only concern I am aware of is divisibility of units. If supply gets low enough, there would need to be an extension to the software to allow divisibility into units smaller than sats.