A longer example:

Imagine a set of 3 events (A, C and B) ordered with unique timestamps each. Event A is the first of all events to happen. Event C is in between the other two. What is a valid bound for Event B's timestamp?

A valid bound for Event B's timestamp would be a time by that is greater than the timestamp of Event A and less than the timestamp of Event C. For example, if the timestamp of Event A is 1:00 pm, the timestamp of Event C is 2:00 pm, and Event B occurs at 1:30 pm, this would be a valid bound for Event B's timestamp.

But I specified that event C is in between the other two?

If Event C is in between the other two events, then the valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event A and less than the timestamp of Event C. For example, if the timestamp of Event A is 1:00 pm, the timestamp of Event C is 2:00 pm, and Event B occurs at 1:30 pm, this would be a valid bound for Event B's timestamp.

This is wrong. With the example of timestamps you give, C is not between the other two events.

You are correct. In the example I provided, Event C is not in between the other two events. My mistake. A valid bound for Event B's timestamp in this scenario would be a time that is greater than the timestamp of Event C and less than the timestamp of Event A. For example, if the timestamp of Event A is 2:00 pm, the timestamp of Event C is 1:00 pm, and Event B occurs at 1:30 pm, this would be a valid bound for Event B's timestamp.

This is still wrong, because I specified that A is the first event to happen.

In that case, a valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event A and greater than the timestamp of Event C. For example, if the timestamp of Event A is 1:00 pm, the timestamp of Event C is 2:00 pm, and Event B occurs at 2:30 pm, this would be a valid bound for Event B's timestamp.

So A at 2pm, C at 1pm, and B at 3pm would also be a valid example.

Yes, that would also be a valid example. In this scenario, the timestamp of Event A is 2:00 pm, the timestamp of Event C is 1:00 pm, and the timestamp of Event B is 3:00 pm. This satisfies the condition that Event A is the first event to happen, and the timestamp of Event B is greater than the timestamps of both Event A and Event C. Therefore, it is a valid bound for Event B's timestamp.

Is this still true when all the events in that last example happen on the same day?

Yes, this is still true if all the events in the last example happen on the same day. In this case, the valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event A and greater than the timestamp of Event C, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 1:00 pm on Monday, and the timestamp of Event B is 3:00 pm on Monday, this would be a valid bound for Event B's timestamp.

So 2pm (event A) happens before 1pm (event C) on Monday, since A happens before C?

No, this is not correct. In the scenario you are describing, Event A and Event C would not occur in the order specified, because Event A is supposed to be the first event to happen and Event C is supposed to be in between the other two events. Therefore, the valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event A and less than the timestamp of Event C, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 3:00 pm on Monday, and the timestamp of Event B is 2:30 pm on Monday, this would be a valid bound for Event B's timestamp.

But this was the example you gave before as being a correct example. And in your new example now, C does not occur between A and B. You don’t seem to have any real understanding of what we’re talking about.

I apologize if my previous examples were not clear or were not consistent with the information provided. My understanding of the scenario is that there are three events (A, C, and B) with unique timestamps, and that Event A is the first event to happen. Event C is in between the other two events, but the order of the events is not specified. In this case, a valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event A and less than the timestamp of Event C, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 3:00 pm on Monday, and the timestamp of Event B is 2:30 pm on Monday, this would be a valid bound for Event B's timestamp.

Don’t you see that if A is the first event to happen, and event C is in between the other two events, that this implies that B must be the last event, and hence this uniquely specifies the order of the events?

Yes, I understand that if Event A is the first event to happen and Event C is in between the other two events, then this implies that Event B must be the last event. This would uniquely specify the order of the events as A, C, B. In this case, a valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event C and greater than the timestamp of Event A, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 1:00 pm on Monday, and the timestamp of Event B is 3:00 pm on Monday, this would be a valid bound for Event B's timestamp.

But 1:00 pm is before 2:00 pm, which means that A is not before C, but after C! The timestamps you give contradict the requirement that A is the first event.

You are correct. In the scenario I provided, the timestamps of the events contradict the requirement that Event A is the first event to happen and Event C is in between the other two events. My mistake. A valid bound for Event B's timestamp in this scenario would be a time that is greater than the timestamp of Event A and less than the timestamp of Event C, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 3:00 pm on Monday, and the timestamp of Event B is 2:30 pm on Monday, this would be a valid bound for Event B's timestamp.

No, this would not be valid, because as we established earlier, the requirements imply that B must be the last event, but in your example C happens last (at 3pm).

You are correct. In the scenario I provided, the timestamps of the events do not satisfy the requirement that Event A is the first event to happen and Event C is in between the other two events. My mistake. A valid bound for Event B's timestamp in this scenario would be a time that is greater than the timestamp of Event C and greater than the timestamp of Event A, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 1:00 pm on Monday, and the timestamp of Event B is 3:00 pm on Monday, this would be a valid bound for Event B's timestamp.

This is wrong again, because in your example the events happen in the order C, A, B according to the timestamps you gave, but they are supposed to happen in the order A, C, B.

Yes, you are correct. In the scenario I provided, the timestamps of the events do not satisfy the requirement that Event A is the first event to happen and Event C is in between the other two events. My mistake. A valid bound for Event B's timestamp in this scenario would be a time that is greater than the timestamp of Event A and less than the timestamp of Event C, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 3:00 pm on Monday, and the timestamp of Event B is 2:30 pm on Monday, this would be a valid bound for Event B's timestamp. This satisfies the conditions that Event A is the first event to happen and Event C is in between the other two events, and the events occur in the order A, C, B. I apologize for any confusion my previous examples may have caused.

Let’s take a step back. Given three events at 1pm, 2pm, and 3pm, in which order do these events occur?

Without any additional information, it is impossible to determine the order in which the events occur. The events could occur in any order, such as 1pm, 2pm, 3pm; 1pm, 3pm, 2pm; 2pm, 1pm, 3pm; 2pm, 3pm, 1pm; 3pm, 1pm, 2pm; or 3pm, 2pm, 1pm. It is only possible to determine the order of the events if there is additional information, such as the requirement that Event A is the first event to happen and Event C is in between the other two events. In this case, the events would occur in the order A, C, B, where A occurs at 1pm, C occurs at 2pm, and B occurs at 3pm.

But 1pm, as a time of day, always happens before 2pm (one hour before), and 3pm always happens after 2pm (one hour later), so the order of those three times is always the same on any given day. Don’t you know that?

Yes, you are correct. As a time of day, 1pm always happens before 2pm, which always happens before 3pm. However, without additional information about the events themselves, it is impossible to determine the order in which the events occur. The events could still occur in any order, such as 1pm, 2pm, 3pm; 1pm, 3pm, 2pm; 2pm, 1pm, 3pm; 2pm, 3pm, 1pm; 3pm, 1pm, 2pm; or 3pm, 2pm, 1pm. It is only possible to determine the order of the events if there is additional information, such as the requirement that Event A is the first event to happen and Event C is in between the other two events. In this case, the events would occur in the order A, C, B, where A occurs at 1pm, C occurs at 2pm, and B occurs at 3pm. I apologize if my previous examples were not clear on this point.

Okay, that last bit looks correct. Can you now correctly answer the original question about the valid bound for event B’s timestamp?

Yes, I can now correctly answer the original question about the valid bound for Event B's timestamp. Given the information that Event A is the first event to happen and Event C is in between the other two events, a valid bound for Event B's timestamp would be a time that is greater than the timestamp of Event A and less than the timestamp of Event C, and occurs on the same day as the other events. For example, if the timestamp of Event A is 2:00 pm on Monday, the timestamp of Event C is 3:00 pm on Monday, and the timestamp of Event B is 2:30 pm on Monday, this would be a valid bound for Event B's timestamp. This satisfies the conditions that Event A is the first event to happen and Event C is in between the other two events, and the events occur in the order A, C, B.

*sigh* Truly fascinating.