Quote from LtKernelPanic
Mycellium is infinite because it'll spread to dirt blocks. All you need to do is silk touch one block and you can farm all you want.
But the dirt blocks themselves are not unlimited. Brobdingnagian in number, perhaps, but not unlimited. Being a non-renewable resource, then given enough time and determination, you could theoretically run out of them. You could mine every dirt block in the map and then there would be no more dirt blocks. Seriously, people, I see this argument just about every other week -- you guys need to look up the definition of the word "infinite." It doesn't just mean "there's a whole lot of them." It means "literally unbounded in number or scale."
The Minecraft world is not literally infinite. It simply can not be, since that would take a computer with infinite processing power, which itself would require an infinite amount of space. And even the best scientists in the world don't even know if there is an infinite amount of space in the entire universe or not. But even if there is, it's certainly not completely filled with computer circuits running a game program.
I repeat, the Minecraft world is not infinite. It has an edge, even coded into the game there is a hard limit past which you can not travel, which occurs about 30 million blocks out from where you spawn near the center of the map.