[youpassbutter]

> The premise that we think we can pack an infinite amount of information into finite space time just feel wrong to me.

Why?

Z = { x | ... -2, -1, 0, 1, 2 ... }

I just packed an infinite amount of information in a couple of characters.

[improbable22]

No, you did not. The point of information is how many different things you can encode, or could have encoded. Among rules about like yours (but reversed, or only the even numbers, etc) this will be about 10.