Abstract
For a long time, many people had thought that the nature should be smooth. It looks as if smoothness describes the universe in more aesthetical and stable way. `Analog', as being closely related to smoothness and infinity, seemed to provide the world eternity and stability. On the other hand, `Digital', although the concept that everything has its fundamental discrete elements had sprung from ancient time, looks rather bizarre and mortal to our analog-lly tamed eyes. It is only when atom was discovered, eventually something `digital' became genuine part of our physical reality. Unlike our physical conception, `digital' objects played main characters in mathematics. Mathematicians have struggled to build `analog' object as a rigous subject. Knowing that objects are composed of discrete elements raise us questions about discreteness of the fabric of space. This article will borrow its ground from set theories which can deal with both analog and digital properly. We will see what the nature should look like in set theories with finite elements and infinite elements. And see how we can use different infinities to understand the physics.
Ryu juno