Cont: Deeper than primes - Continuation 2

[doronshadmi]

Right, so. Doronshadmi has effectively admitted that he cannot define "successor".

Nonpareil effectively demonstrates that its used reasoning can't handle with http://www.internationalskeptics.com/forums/showpost.php?p=11297273&postcount=1593.

Can we end the thread now?

So, the thread has to be closed because Nonpareil's reasoning can't handle with it.

What a poor attitude.

Nonpareil, did you try to deal with your avatar (http://www.internationalskeptics.com/forums/showpost.php?p=11264137&postcount=1251)?

 

[jsfisher]

There is no much to say to a person who uses a reasoning that can't distinguish between "{} = {}" and "({X} IsSuccessorOf X) OR ({X} ~IsSuccessorOf X)".

Your version of reasoning, much like your inventions in terminology, lacks meaning. I'd ask you to define how logic works in doronetics, but it is well-established how well you can handle definitions. I accept that would not be a fruitful path to pursue.

Enjoy your fantasy world.

 

[doronshadmi]

Your version of reasoning, much like your inventions in terminology, lacks meaning. I'd ask you to define how logic works in doronetics, but it is well-established how well you can handle definitions. I accept that would not be a fruitful path to pursue.

Enjoy your fantasy world.

Another non-informative post of you that avoids real discussion about http://www.internationalskeptics.com/forums/showpost.php?p=11298764&postcount=1600.

 

[Little 10 Toes]

Yet you still can't provide a definition to successor. Why is that?

 

[doronshadmi]

Yet you still can't provide a definition to successor. Why is that?

Being a successor is an optional (non-essential) property of primitive {X}.

If this optional (non-essential) property of primitive {X} is used, the optional (non-essential) property of primitive X is incompleteness.

More details are found in http://www.internationalskeptics.com/forums/showpost.php?p=11294638&postcount=1581 (and its links).

Also http://www.internationalskeptics.com/forums/showpost.php?p=11271084&postcount=1374 and http://www.internationalskeptics.com/forums/showpost.php?p=11297273&postcount=1593 are straightforward about the issue at hand.

 

[Nonpareil]

Being a successor is an optional (non-essential) property of primitive {X}.

If this optional (non-essential) property of primitive {X} is used, the optional (non-essential) property of primitive X is incompleteness.

You said this.

You still have not told us how to tell if {X} is the successor of X. As it stands, the definition is "whenever doron wants it to be".

 

[doronshadmi]

You still have not told us how to tell if {X} is the successor of X.

You are still using a reasoning that does not distinguish between primitives and their optional (non-essential) properties.

By using a reasoning that enables one to distinguish between primitives and their optional (non-essential) properties, the wff ({X} IsSuccessorOf X) OR ({X} ~IsSuccessorOf X) is a useful definition, as already demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=11300215&postcount=1605.

Also please do not ignore http://www.internationalskeptics.com/forums/showpost.php?p=11298816&postcount=1601.

 

[doronshadmi]

Some post on Standard Mathematics.

Let's talk about a function such that for each member of set X there is exactly one member of set Y that is mapped with it, so |Y| > OR = |X|.

We know that order has no influence on X --> Y among finite sets.

But is this also the case among infinite sets?

In this post, I am using the standard notion that the cardinality of N is aleph₀.

It is easy to show that there is bijection between the set of all even numbers (which is a proper subset of the set of all natural numbers) and the set of all natural numbers, for example:

2 --> 1
4 --> 2
6 --> 3
...

But what if order is used among the members of the set of all natural numbers, such that all even numbers appear first, as follows? :

2 --> 2
4 --> 4
6 --> 6
...

In this case there is no bijection between the set of all even numbers (which is a proper subset of the set of all natural numbers) and the set of all natural numbers (no odd number is in the range of all even numbers).

So what Standard Mathematics says about the influence of order on the mapping between those two infinite sets?

 

[jsfisher]

So what Standard Mathematics says about the influence of order on the mapping between those two infinite sets?

Mappings are unordered, so order has no influence.

 

[doronshadmi]

Mappings are unordered, so order has no influence.

Here is the current result of google search after "Mappings are unordered":

https://www.google.co.il/?gfe_rd=cr...gws_rd=ssl#q="Mappings+are+unordered"&start=0

Also Here is the current result of google scholar search after "Mappings are unordered":

https://scholar.google.co.il/scholar?hl=en&q="Mappings+are+unordered"&btnG=&as_sdt=1,5&as_sdtp=


So "Mappings are unordered" is not so helpful, please try something else.

----------------

The search result of "functions are unordered" is even less helpful:

https://www.google.co.il/?gfe_rd=cr&ei=cLxIV7zpJ4bu8wfig6fQDA&gws_rd=ssl#q="functions+are+unordered"

https://scholar.google.co.il/scholar?hl=en&q="functions+are+unordered"&btnG=&as_sdt=1,5&as_sdtp=

(Please be aware that "Mappings in VDM++ are finite", as seen in page 3 of https://www.google.co.il/url?sa=t&r...sg=AFQjCNGQNfBRu1mVgYVSXMTBQJJF5wKa1g&cad=rja. More about VDM is seen in https://en.wikipedia.org/wiki/Vienna_Development_Method)

 

[jsfisher]

Here is the current result of google search after "Mappings are unordered"

If there is a point you are trying to make, state it. The rest of us are not able to guess what you may think significant from your adventure with google.

You asked about the influence of order on mappings. Since mappings are not ordered, your question is meaningless: Order has no influence on mappings.

Your turn.

 

[doronshadmi]

If there is a point you are trying to make, state it.

Being ordered OR unordered is an optional (non-essential) property of being a mapping.

For being a mapping (in the minimal standard sense) all is needed is a unique member of the domain AND a unique member of the codomain.

So once again you have no argument.

(b.t.w maybe you will find http://arxiv.org/pdf/1502.06936v2.pdf interesting. I did not look at it carefully, yet)

 

[jsfisher]

Being ordered OR unordered is an optional (non-essential) property of being a mapping.

You're making stuff up right from the gate. This fantastical world of yours -- don't know what it is, but it isn't Mathematics.

 

[doronshadmi]

You're making stuff up right from the gate. This fantastical world of yours -- don't know what it is, but it isn't Mathematics.

You are invited to support your argument that being unordered is a must have property of mapping.

http://www.internationalskeptics.com/forums/showpost.php?p=11302140&postcount=1610 may be a good start.

Generally, your view of what is considered as Mathematics is very narrow.

 

[jsfisher]

You are invited to support your argument that being unordered is a must have property of mapping.

There is nothing to argue. As much as you seem to like fighting definitions, they are not up for debate.

 

[Little 10 Toes]

Please provide the definition of successor doronshadmi.

 

[doronshadmi]

There is nothing to argue. As much as you seem to like fighting definitions, they are not up for debate.

At least support your argument that "Mappings are unordered" such that being unordered is an essential (must have) property in order to mathematically be considered as mapping in the first place, by providing a link to a professional academic source on this subject.

Since the current subject (seen in http://www.internationalskeptics.com/forums/showpost.php?p=11301653&postcount=1608) is in the domain of Standard Mathematics, such a source can be provided by you, so please support your "Mappings are unordered" argument.

I did not find such source, as seen in http://www.internationalskeptics.com/forums/showpost.php?p=11302140&postcount=1610, so please use your skills and provide such source.

 

[doronshadmi]

Please provide the definition of successor doronshadmi.

http://www.internationalskeptics.com/forums/showpost.php?p=11300215&postcount=1605.

 

[Little 10 Toes]

That post does not define successor. Try again.

 

[jsfisher]

Since the current subject....

You really should finish the previous current subject before you flitter off to a new one. The world still awaits your definition for successor and complete.