/sci/ - Science & Math

>>14952791
At least countably many:
Consider Z with one, two, three, ... points at the end.
At most countably many:
False. Take any sequence a_i of zeros and ones, and take the following order type:
whenever you have a 0, put one isolated points to the right, whenever you have a 1, put a copy of Z to the right and an isolated point to the right of it. Every two such order types are distinct, since you may read off the digits by:
- first digit is 0 if no first element. Remove the initial segment until the first element without predecessor
- first digit is 1 if order has first element. Remove it.
Continue the process with the order that is left.