Consider these definitions:

I think, there is a mistake in this definition of well-ordering which makes the latter impossible.

Am I right?

1 hour ago, Genady said:

Consider these definitions:

I think, there is a mistake in this definition of well-ordering which makes the latter impossible.

Am I right?

I'm more and more rusty on these things with every passing month, but doesn't the latter require S to be a closed set to be true?

At the very least it requires a topology, if I remember correctly. Open subsets don't necessarily have minimal elements.

I remember I still have a quiz/riddle on divisibility that you posed months ago pending. I'm sorry about that. Maybe you published the solution?

24 minutes ago, joigus said:

I'm more and more rusty on these things with every passing month, but doesn't the latter require S to be a closed set to be true?

At the very least it requires a topology, if I remember correctly. Open subsets don't necessarily have minimal elements.

I remember I still have a quiz/riddle on divisibility that you posed months ago pending. I'm sorry about that. Maybe you published the solution?

No topology here. This is pure set theory, more specifically, ZFC.

There is no requirement that a set has to be well-ordered. It is only a definition, when it is. I claim that the definition as stated is meaningless, i.e., no set so well-ordered exists.

(I don't remember which quiz/riddle on divisibility I posed months ago ☹️ )

P.S. I like your "Location." 🙂

20 hours ago, Genady said:

Am I right?

No. (Check your notes or references about basics of algebra.)

19 hours ago, joigus said:

I'm more and more rusty on these things with every passing month, but doesn't the latter require S to be a closed set to be true?

does it mention or tell about closed or open set?

19 hours ago, joigus said:

Open subsets don't necessarily have minimal elements.

also consider, does a well ordered set have to be open set?

19 hours ago, joigus said:

if I remember correctly.

I opinionate in negative.

Edited 23 minutes ago23 min by ahmet