• Security incident: ISF was recently accessed by intruders. Please change your password, and change it anywhere else you used it. Read more

Cont: Deeper than primes - Continuation 2

Status
Not open for further replies.
doronshadmi said:
By prevent the existence of incomplete sets.
Click to expand...

That is yet to be seen. First, you need to give meaning to the term "incomplete set", and then you must show its relationship to that tautology involving your variation on successor.
 
jsfisher said:
Perhaps you could highlight for us where in that post you define set completeness. I don't know how I could have missed it.

Hopefully it is something like, "For all S, Iscompleted(S) iff ...."
Click to expand...
A complete set is not defined by {y}$y for any y.

An incomplete set is defined by {y}$y for any y.

Already defined in http://www.internationalskeptics.com/forums/showpost.php?p=11263283&postcount=1235, http://www.internationalskeptics.com/forums/showpost.php?p=11266069&postcount=1275 and explained "externally" and "internally" in http://www.internationalskeptics.com/forums/showpost.php?p=11264035&postcount=1249.
 
Last edited:
doronshadmi said:
A complete set is not defined by {y}$y for any y.

An incomplete set is defined by {y}$y for any y.
Click to expand...


Still not seeing this part: "For all S, Iscompleted(S) iff ...." You know, that math stuff.
 
Last edited:
Last edited:
jsfisher said:
Given how you've defined your non-standard successor relation, all sets are what you've defined to be incomplete.
Click to expand...
You are still missing the simple notion of "next" (as seen in http://www.internationalskeptics.com/forums/showpost.php?p=11265933&postcount=1272).

Once again.

If {S} not-$ for any S, then S is complete.

If {S} $ for any S, then S is incomplete.

Please be aware about http://www.internationalskeptics.com/forums/showpost.php?p=11267576&postcount=1296, where you wrongly recognize {S}$S as a tautology, exactly because you are missing {S}not-$S.
 
"is a member of" is not a tautology because also "is not a member of" holds.

"is a successor of" is not a tautology because also "is not a successor of" holds.
 
Last edited:
doronshadmi said:
You are still missing the simple notion of "next" ...
Click to expand...

"Next" is part of neither your definition for your non-standard successor relation nor for your set-completeness attribute.

Perhaps you could show us a set that would be complete under your definitions. Is {A, B} complete?
 
More generally, one is not forced to define only {S}$S exactly because also {S}not-$S is defined.
 
jsfisher said:
"Next" is part of neither your definition for your non-standard successor relation nor for your set-completeness attribute.
Click to expand...
"next" is the idea at the basis of my successor relation (and also at the basis of my set-completeness attribute), exactly as "belongs" is the idea at the basis of membership relation.

jsfisher said:
Perhaps you could show us a set that would be complete under your definitions. Is {A, B} complete?
Click to expand...
Yes, and N is "internally" incomplete because it is defined as {{y}$y}, as already shown in http://www.internationalskeptics.com/forums/showpost.php?p=11266617&postcount=1277.
 
Status
Not open for further replies.

Share this page

ISF - Join now!

Every member here is approved by hand. No bots, no spam, just people who care about evidence and honest debate.

Membership is free!

Create your free account

Back
Top Bottom