How thick is the "Flat Earth"

I've read many forums. Many debates. Many idiotic assertions from everyone. I have yet to see this problem addressed. For once, let us say the earth is flat. Does this mean it is 2 dimensional? What is on the other side? (I am, for the time being, disregarding JRoweSkeptic's dual earth theory.) How can we mine thousands of ores under the earth if it is a 2-dimensional surface?

I am a round earther, but I have only met one flat earther who thinks the Universe is 2D.  There is also a flat earther who believes that mountains and oceans don't exist, but other then that the flat earthers have managed to gain at least a toddler level understanding of 3D space in their brain cell.

I realise that. But even still, a flat earth is flat. What, does it reach the bottom of the universe like that bloody stupid infinite earth theory? I know round-earthers like myself will think I'm talking bollocks but there's going to be someone that thinks the earth is 2D. I was reading the non-existent mountains guy about 5 minutes before I posted this. That's what gave me the idea.