empty set
The empty set {} contains no element, nothing whatsoever.
Next we consider the set {{}}, which contains the empty set as its only element.
Then the set { {}, {{}} } which contains two elements and so on and so forth.
We assign the symbols 0, 1, 2, ... to these sets for convenience.
This is of course the standard definition of the natural numbers N as given by von Neumann; Once we have N then Z, Q, R, C etc. follow from N more or less in the usual manner.
I only mention it because some people believe that all physics is really just math.
But if "external physical reality is assumed to be purely mathematical" then all reality is based on the empty set.
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3 comments:
Wolfgang,
Below is a link to a colloquia given by Charles Bennett at KITP. I think it is at least peripherally related to some of the things you seem to like to think about.
http://online.itp.ucsb.edu/online/colloq/bennett1/rm/flash.html
Lee,
thank you for the link.
Quantum Information and ambiguity of the past ... seems interesting; I will watch it.
i remember seeing that proof from a high school math teacher (great teacher). he promoted it as creating numbers out of nothing.
and then being dissapointed by how unmagical it was.
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