I have an exercise that asks me for 15 non-isomorphic well order types of natural numbers, I have some, can you help me with other well uncommon orders?
Thank you
2026-03-26 01:10:46.1774487446
Well order of naturals
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$\omega_0$ + n for all n in N are equinumerous to N
well ordered and not pairwise order isomorphic.
1,2,3,... 0; 2,3,4,... 0,1; and so on.
$\omega_0$ + $\omega_0$ + n is yet another bunch of examples.
For example placing all of the even numbers in order before all of the odd numbers in order. 0,2,3,... 1,3,5,...
This idea can be continued indefinitely
0,3,6,... 1,4,7,... 2,5.8,... and so forth for other sets of integers modulus n.
But wait, there are scads more based upon even larger ordinals such as $\omega_0 × \omega_0$. Here's a small wow
0 2 5 ...
1 4 ...
3 ...
•••
For bigger wows, go for higher powers of $\omega_0$.
Beyond all of those are colossal wowies.