[FOM] Quine Atom x={x}
Axiomize@aol.com
Axiomize at aol.com
Fri Sep 6 14:24:25 EDT 2002
Define the following three functions from the set of functions to the set of
sets of functions. That is, each takes in one or two functions and returns a
set of functions:
s1(x) = { x(x) }
s2(x,y) = { x(x,y) }
s3(x) = { x(x), 0 }
For example, s1 takes in function x, applies x to x, and returns the set
containing the value of x applied to x.
1. Consider the following specific set:
s1(s1) = { s1(s1) }
Thus s1(s1) is a Quine atom, a set that contains only itself.
2. Consider the following function s4:
s4(x) = s2(s2,x) = { s2(s2,x) }
Thus for each x function s4 returns a set that is a Quine atom. Is there
more than one value in the range of s4?
3. Consider the following set:
s3(s3) = { s3(s3), 0 }
Then s3(s3) is a solution to the equation x={x,0}.
Comments?
Charlie Volkstorf
Cambridge, MA
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