Cont: Deeper than primes - Continuation 2

[doronshadmi]

People didn't ask you to define 'optional property'. They ask you to define 'successor', which you still have not done.

It is done since being a successor OR not being a successor are true options of {X}.

Why are you doing your "best" in order to avoid http://www.internationalskeptics.com/forums/showpost.php?p=11294638&postcount=1581?

 

[doronshadmi]

Why are x and ~x both true? Contradictions are (or can be) true in doronetics?

It is x OR ~x.


You are wrongly still get it as "x AND ~x", as seen the highlighted part of your question.

 

[MetalPig]

It is x OR ~x.


You are wrongly still get it as "x AND ~x", as seen the highlighted part of your question.

Yes, because you put a T under both x and ~x:

What you say is irrelevant to ({X} IsSuccessorOf X is a true option) OR ({X} ~IsSuccessorOf X is a true option) and this is exactly the meaning of

x OR ~x
-------
[HILITE]T     T -[/HILITE]--> T

 

[doronshadmi]

Yes, because you put a T under both x and ~x:

It is under x OR ~x.

You are still stuck at x AND ~x (as seen in the highlighted part of your reply).

Once again, why are you doing your "best" in order to avoid http://www.internationalskeptics.com/forums/showpost.php?p=11294638&postcount=1581?

 

[Little 10 Toes]

It is done since being a successor OR not being a successor are true options of {X}.

Why are you doing your "best" in order to avoid http://www.internationalskeptics.com/forums/showpost.php?p=11294638&postcount=1581?

Define successor. So far you haven't. You have told us what it is, but have not defined it.

Example: A shemgrik is a holiday food. I have not defined what shemgrik is.

 

[MetalPig]

It is under x OR ~x.

Then why are there 2 T's under x OR ~x ?

You are still stuck at x AND ~x (as seen in the highlighted part of your reply).

Only if you take it out of context.

 

[doronshadmi]

Example: A shemgrik is a holiday food. I have not defined what shemgrik is.

Wrong example, since shemgrik is optional it can't be defined in terms of a particular holiday food.

 

[MetalPig]

Wrong example, since shemgrik is optional it can't be defined in terms of a particular holiday food.

shemgrik is a holiday food XOR shemgrik is not a holiday food

That doesn't tell us anything about what shemgrik is.

 

[doronshadmi]

Then why are there 2 T's under x OR ~x ?

Because (being a successor) OR (not being a successor) are both true options of {X}, and this logical fact is the 4^TH part of OR truth table

 x OR ~x
--------
~T    ~T --> ~T
~T     T -->  T
 T    ~T -->  T
[HILITE] T     T -->  T[/HILITE]

More details are already given in http://www.internationalskeptics.com/forums/showpost.php?p=11334321&postcount=1688.

Only if you take it out of context.

AND truth table is out of the context of OR truth table, so please avoid using your "x and ~x" once again.

 

[doronshadmi]

shemgrik is a holiday food XOR shemgrik is not a holiday food

That doesn't tell us anything about what shemgrik is.

Now you are forcing XOR truth table on OR truth table.

Why are you doing that?

 

[jsfisher]

Doron has trouble with evaluating expression that require more than one step. This has come up in the past many times in many different forms.

Building a truth table for ~X is no problem because there is only one step from possible values of X to evaluation of the expression ~X.

Even X AND Y isn't a problem since there is only one step from each of the four possible combination of values for X and Y to evaluation of the expression of X AND Y.

However, X OR ~X requires two steps, and so in all breaks down into nonsense.

 

[doronshadmi]

EDIT:

However, X OR ~X requires two steps,

Please demonstrate it.

and so in all breaks down into nonsense.

Also do not forget that you defined ({X} IsSeccessorOf X) OR ({X} ~IsSeccessorOf X) as a tautology, so nothing logically breaks down into nonsense even by your own reasoning.

 

[doronshadmi]

This has come up in the past many times in many different forms.

Where exactly?

 

[jsfisher]

Please demonstrate it.

Two of my posts back.

Also do not forget that you defined ({X} IsSeccessorOf X) OR ({X} ~IsSeccessorOf X) as a tautology, so nothing logically breaks down into nonsense even by your own reasoning.

No, I did not. I said it was a tautology, which is a comment on its truth value, not its definition.

 

[jsfisher]

Where exactly?

Do you want to go all the way back to your earliest posts about hidden assumptions? You did the same thing with truth tables and boolean logic back then. Or perhaps we should revisit your insistence that a set is the union of its members? Or maybe your rejection of Cantor's Theorem because you failed to connect the proof steps?

Let's not, though. It would be pointless. You are still in the same rut.

 

[doronshadmi]

Two of my posts back.

And as usual you avoid the reply in http://www.internationalskeptics.com/forums/showpost.php?p=11335671&postcount=1693.

No, I did not. I said it was a tautology, which is a comment on its truth value, not its definition.

Again, by jsfisheretics being optional is not an option and as a result you are missing the issue at hand.

 

[doronshadmi]

Do you want to go all the way back to your earliest posts about hidden assumptions? You did the same thing with truth tables and boolean logic back then.

Please demonstrate that what I said then, is related to the current issue at hand.

Or perhaps we should revisit your insistence that a set is the union of its members?

A set includes the members (if exist) of unioned sets, where one of the cases is X u X.

Or maybe your rejection of Cantor's Theorem because you failed to connect the proof steps?

Are you kidding?

Since no infinite collection is complete, Cantorian set theory has no mathematical basis.

Let's not, though. It would be pointless. You are still in the same rut.

You are living in the past.

 

[zooterkin]

In the set of natural numbers, what is the successor of 3? Show how you determined this using your definition.

 

[doronshadmi]

In the set of natural numbers, what is the successor of 3? Show how you determined this using your definition.

Being a successor, according to my definition, is not some member of a given set.

"In the set of natural numbers" still uses Successor(x) = x u {x}.

By using {x} as an optional successor of x there is a set of natural numbers that may be complete if {x} is not a successor of x OR incomplete if {x} is a successor of x.

In case of, for example, set {2,1,4,3,...}, that is notated as 4 is different than that is notated as 3, by that is notated as 1.

 

[MetalPig]

Now you are forcing XOR truth table on OR truth table.

Why are you doing that?

Because in the real world, contradictions are false.
There is no force, just logic.