Is this true, if so is it obvious?

  • Thread starter Dragonfall
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In summary, there is no proper class such that every totally ordered set is isomorphic to a subclass of it. The class of all sets satisfies this requirement, but it is not considered a proper class.
  • #1
Dragonfall
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There is no proper class such X such that every totally ordered set is isomorphic to a subclass of X.

I'm using "proper class" and "isomorphic" rather liberally here, but you can assume them to be formulas in ZFC, or something.
 
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  • #2
? What about the class of all sets? Every set is a subclass of that, so certainly every totally ordered set is a subclass of it... Also, if you want something stricter; since the class of all sets is a class, you can consider the class of all totally ordered sets. Is your question whether or not that is a proper class? I'd think that it would be, but the way you asked your question, it sounds like the class of all sets should satisfy your requirement.

Maybe I'm misunderstanding something here?
 
Last edited:
  • #3
No, you're right.
 

1. Is this true?

This question is often asked when someone hears or reads information that they are unsure about. It is important to critically evaluate the source and evidence before determining if something is true or not.

2. If so, is it obvious?

This question usually follows the first one and is asking for clarification on the level of certainty or evidence for the information. Even if something is true, it may not be obvious or easily understood without further explanation or context.

3. How do you know if something is true?

This is a common question when trying to determine the validity of information. As a scientist, it is important to use the scientific method and rely on evidence, data, and peer-reviewed research to support claims and conclusions.

4. Are there any biases in determining if something is true?

Yes, biases can affect our perceptions and judgments about what is true or not. It is important to be aware of our own biases and try to approach information objectively and critically.

5. Can something be true and still be debatable?

Yes, truth can be subjective and open to interpretation. In some cases, there may be multiple truths or perspectives on a topic. It is important to consider different viewpoints and evidence when evaluating the truthfulness of information.

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