>>12701695Why?
Could properties be generated by some function on a set. I am thinking right now of a set constructed by functions on integers.
S =
P0: Integer
P1: f(n) = n
P2: f(n) = n + 1
...
Px: f(n) = n + (x - 1)
Infinity would be the only "number" that matches the criteria of this set of infinite properties. Of course, i don't like that solution so it is better to reformulate it as some converging series. It should be obvious that any number can be represented by an infinite number of converging series, but one example can be taken for the 0 point on a parabola. There is infinite accommodation for changing the parameters in a parabola without changing the point 0,0.
Further configuring can be done for other numbers as well, but they may not be all be algorithmic.
This reasoning isn't really the point at hand.
If what you are saying is true, then how are these conditions handled? Is it considered that there is some simpler property which describes a collection of infinite properties?
Another example, suppose digits of pi
PI(1) = 3
PI(2) = 3.1
...
PI(?) = ?
And then take all approximations of ? which match to kth digit. To fit this set each approximation will have the property of starting with 3; however on the set of PI, PI(n) has the property of being a member of each of those sets and it also shares all of these approximating functions of every other member of P(n+1), though the reverse is not true.
