Hi!
I am browsing the articles about well-ordered sets and tree (set theory). I am just asking myself what's the difference between well-ordered sets and the natural numbers.
I imagine the following set, with the natural "<" relation. (NN_0 = the natural numbers, with zero)
M = { m + k/(k+1) | m, k in NN_0 }
Is (M, <) a well-ordered set? Is it a tree, in the set-theoretic sense? Every subset has a smallest member, right?
If so, it would be helpful as an example, to show how the concept of well ordering does not imply an ordering like the natural numbers have..
Regards, Schneemann.. |
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