- #1
Mecha Miles
- 2
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So I'm working on a personal project, and I have most of the details worked out, but I'm having difficulty expressing an idea in precise terms.
Premise:
We start with a set which has only itself as an element, which results in the following infinite regress:
{{{...}}}
Now what I would like to do is create a bijection between this infinite regress and some general singleton set.
For example: Say we have a set, call it S, such that S={1}. Now I want to create a bijection between S and the set above such that the resulting set is {...1,1,1,1...}.
How can I express this relationship in rigorous terms -with notation common to set theory.
Any thoughts from the community would be very appreciated.
Shalom
Premise:
We start with a set which has only itself as an element, which results in the following infinite regress:
{{{...}}}
Now what I would like to do is create a bijection between this infinite regress and some general singleton set.
For example: Say we have a set, call it S, such that S={1}. Now I want to create a bijection between S and the set above such that the resulting set is {...1,1,1,1...}.
How can I express this relationship in rigorous terms -with notation common to set theory.
Any thoughts from the community would be very appreciated.
Shalom