Deeper than primes - Continuation

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doronshadmi said:
EDIT:

realpaladin, all you have is to realize that a function with no output is a valid mathematical expression.
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Nothing posted after the several blunders contained in this one sentence matters since it is predicated on errors.

Fix this, Doron, before we can discuss anything that follows.
 
realpaladin said:
Show me *how* anyone could deduce that from my reply.
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Maybe I am wrong and you are actually agree that a function with no output at all (it returns nothing) is a valid mathematical expression.

In this case, by using such a function you are enable to follow my posts, but it seems that all you get is a word salad.

Moreover, you wrote
realpaladin said:
Doron, if you just add your temporal dimension (ie the customer *left*) to the mapping *function * from the start, you will see that nothing spectacular is happening here.
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But you see realpaladin, nothing is temporal here and also no customer *left* in

1 → 1
2 →
3 → 2
4 → 3
5 → 4
...

What we actually have here is a function with no output at all (it returns nothing).

As long as you do not get the mathematical validity of such function, you have no basis to say any meaningful thing about the discussed subject.

So in order to be completely sure about your position of this subject I will ask you a simple question:

Do you agree that a function that does not have any output at all (it returns nothing) is a valid mathematical expression?

Please answer only by yes or no.
 
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jsfisher said:
Nothing posted after the several blunders contained in this one sentence matters since it is predicated on errors.

Fix this, Doron, before we can discuss anything that follows.
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As I see it, the blunder is your disagreement about the mathematical validity of a function that does not have any output at all (it returns nothing).

As long as this is your position you don't have any meaningful thing to say about the discussed subject.

So in order to be completely sure about your position of this subject I will also ask you a simple question:

Do you agree that a function that does not have any output at all (it returns nothing) is a valid mathematical expression?

Please answer only by yes or no.
 
doronshadmi said:
Maybe I am wrong and you are actually agree that a function with no output at all (it returns nothing) is a valid mathematical expression.
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Doron, your failure to answer is telltale to your abysmal reading comprehension.

As for something having return values or not... Come on, you haven't been keeping abreast of any programming language, logic representation or mathematical notations.

If you had, you would have found out that what you are *trying * to claim is either old hat/old news or plain wrong.

Your choice.
 
realpaladin said:
Doron, your failure to answer is telltale to your abysmal reading comprehension.

As for something having return values or not... Come on, you haven't been keeping abreast of any programming language, logic representation or mathematical notations.

If you had, you would have found out that what you are *trying * to claim is either old hat/old news or plain wrong.

Your choice.
Click to expand...

realpaladin said:
How like a child you are.
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Evasion has been noted about http://www.internationalskeptics.com/forums/showpost.php?p=9713580&postcount=2884.
 
doronshadmi said:
As I see it, the blunder is your disagreement about the mathematical validity of a function that does not have any output at all (it returns nothing).
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If you reviewed the actual meaning of the term, function, in Mathematics, you might finally come to grips with reality. The blunder continues to be yours.


Doron, if you cannot get even the simplest of things right, how can anyone take anything else you say seriously?
 
Doron, really, nobody cares about your opinions or whether or not you 'note' things.

As long as your grasp of what is communicated to you, be it in academic papers, be it in this thread, is so horrendous that Rowan Atkinson could play it verbatim as a hit character, the very first thing you, and only you, need to demonstrate is the simple ability to participate in a discussion.

Until that time, nothing you write can be of any worth to anyone, save for holiday dinner anecdotes.
 
jsfisher said:
If you reviewed the actual meaning of the term, function, in Mathematics, you might finally come to grips with reality. The blunder continues to be yours.


Doron, if you cannot get even the simplest of things right, how can anyone take anything else you say seriously?
Click to expand...
Do you agree that a function that does not have any output at all (it returns nothing) is a valid mathematical expression?

Please answer only by yes or no.
 
doronshadmi said:
Do you agree that a function that does not have any output at all (it returns nothing) is a valid mathematical expression?
Click to expand...

Perhaps this will help you understand why your question is idiotic:

wikipedia said:
A function f from X to Y is a subset of the cartesian product X × Y subject to the following condition: every element of X is the first component of one and only one ordered pair in the subset.
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jsfisher said:
Perhaps this will help you understand why your question is idiotic:
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EDIT:

So your answer is *no*, since according to your used definition of a function, ordered pairs of the form (x,y) are involved, such that x or y are always place holders of something (as done by René Descartes).

By being limited to such definition of a function, which claims that a function is some ordered pair of Cartesian product (as done by René Descartes), there is no wonder that a case like (x,) seems to be idiotic.

But you see jsfisher, in this philosophical forum we do not deal only with the current agreements among mathematicians about mathematical subjects, but we also deal with the ability to expand given mathematical subjects beyond thier current understanding and use (where in this case the discussed subject is the definition of a function), where the expansion is done from within (by mutation) when new insights of the discussed mathematical subjects are involved.

All along this philosophical thread you claim that definitions are not subjects for changing, and this claim is not a mathematical claim, but it is a philosophical claim.

It seems that you do not understand that your claims, in this case, are philosophical claims.

Let us use some analogy, in order to address better the above.

According to the Geocentric model the Earth is positioned in the center of orbits, where these orbits have shapes of perfect circles.

According to the current Heliocentric model, the sun is positioned in a given center of several elliptic orbits around it.

According to jsfisher's philosophy, concepts like center or orbit need new definitions, because these concepts are already "well-defined" by the Geocentric model.

But as you see, physicists use concepts like center or orbit in both models without giving them new definitions, but they give them new interpretations, which enable to conclude that the Geocentric model is wrong (end this conclusion is possible in the first place exactly because no new definitions to concepts like center or orbit, are given in the current Heliocentric model.)

The demand of "pure" mathematicians to provide new definition to any change, establish mathematical environment of isolated context-dependent-only "worlds", which easily enable to miss new insights about possible discussed subjects, and in this case, a function without any output at all (it returns nothing).
 
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doronshadmi said:
Please explain your expression above, in details.
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- You write narcissistic / autistic: all you ever write is your point of view and keep pushing that like a bulldozer
- You are not able to pick up arguments by another party and respond to them
- You are unable to *explain * why the other party is incorrect. All you ever do is state they are incorrect and then repeat your point of view.

If you really grasp the material, then you would be able to explain in detail why the other arguments are wrong.

However you never do, you only repeat yours and sprinkle it with "evasion noted", "it shows "," it is clear ".
But those phrases look so out of place that all anyone can do is think that you are a science wannabe.

Jsfisher and I (and others) have given you examples on how to respond in the course of 7 years, but you keep being the autist.
 
doronshadmi said:
EDIT:

So your answer is *no*, since according to your used definition of a function, ordered pairs of the form (x,y) are involved, such that x or y are always place holders of something
Click to expand...

It does not matter what follows this sentence, because you can not take someone serious that does childish things like the yes/no thing.
 
realpaladin said:
- You write narcissistic / autistic: all you ever write is your point of view and keep pushing that like a bulldozer.
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Possible novel ideas may be interpreted as narcissistic / autistic from the traditional point of view, so?

realpaladin said:
- You are not able to pick up arguments by another party and respond to them
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I don't understand this part, please write it more clearly.

realpaladin said:
- You are unable to *explain * why the other party is incorrect.
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Well, for example, I showed that
realpaladin said:
Doron, if you just add your temporal dimension (ie the customer *left*) to the mapping *function * from the start, you will see that nothing spectacular is happening here.
Click to expand...
is incorrect simply because nothing is temporal and also no customer *left* in

1 → 1
2 →
3 → 2
4 → 3
5 → 4
...

The problem is that you do not understand that your arguments (in the quoted example above) are incorrect, in this case.

realpaladin said:
If you really grasp the material, then you would be able to explain in detail why the other arguments are wrong.
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It is done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9711871&postcount=2867 , http://www.internationalskeptics.com/forums/showpost.php?p=9712768&postcount=2877 or http://www.internationalskeptics.com/forums/showpost.php?p=9715149&postcount=2894.

realpaladin said:
However you never do, you only repeat yours and sprinkle it with "evasion noted", "it shows "," it is clear ".
But those phrases look so out of place that all anyone can do is think that you are a science wannabe.
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I believe you that this is all you are able to get from my replies. One possible option is that they are novel (they can't be comprehended by using the traditional point of view of the discussed subject).

realpaladin said:
Jsfisher and I (and others) have given you examples on how to respond in the course of 7 years, but you keep being the autist.
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The given examples are all done by using the traditional points of view of the discussed subjects, so?
 
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I am going to enjoy my holidays.

Merry Christmas Doron, JSFisher, !Kaggen, Iaca and everyone else!

Talk to you in the New Year!

:xsmiley:xmas:xmrsclaus
 
realpaladin said:
It does not matter what follows this sentence, because you can not take someone serious that does childish things like the yes/no thing.
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Do you claim that the inability to answer by *yes* or *no* marks someone as non-childish?

Do you also claim that no question can be answered by using *yes* or *no*?
 
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doronshadmi said:
EDIT:

So your answer is *no*, since according to your used definition of a function, ordered pairs of the form (x,y) are involved, such that x or y are always place holders of something
Click to expand...

Pesky things, definitions. You don't get to just change them on a whim.

...(as done by René Descartes).
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Nope. It would probably be best for you if you not pretend to know more about a subject than you really do.

...
But you see jsfisher, in this philosophical forum we do not deal only with the current agreements among mathematicians about mathematical subjects, but we also deal with the ability to expand given mathematical subjects beyond thier current understanding and use (where in this case the discussed subject is the definition of a function), where the expansion is done from within (by mutation) when new insights of the discussed mathematical subjects are involved.
Click to expand...

Expand all you like, just don't pretend you are talking about mathematical functions. You are talking about something that isn't a function, and your valueless insights are for things that aren't functions.
 
doronshadmi said:
Do you claim that the inability to answer by *yes* or *no* marks someone as non-childish?

Do you also claim that no question can be answered by using *yes* or *no*?
Click to expand...

You forgot to add, "Please answer with just either 'yes' or 'no'."
 
jsfisher said:
You are talking about something that isn't a function, and your valueless insights are for things that aren't functions.
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I am talking about something that is a function, and your limited insights (and therefore limited definitions) of functions are valueless in this case.

Ok, let's play with the pairs' game, by using an expression of the form (x,y) as follows:

The outer "(" and ")" define Hilbert's hotel environment.

x defines the name of a given room in that environment.

y defines a room in that environment such that it can be without any visitor (notated by ()) OR with exactly one visitor (notated by (n), where n is a placeholder for some visitor's name).

The following case of the pairs' game

(1,(1))
(2,())
(3,(2))
(4,(3))
(5,(4))
...

rigorously shows that even if there is 1-to-1 and onto from the names of the rooms to the names of the visitors, there is also at least one room beyond the range of the visitors.

Is this pairs' game (as played above) can be addressed by jsfisher's traditional definition of function?
 
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doronshadmi said:
I am talking about something that is a function, and your limited insights (and therefore limited definitions) of functions are valueless in this case.
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Definitions are supposed to limit; that's one of the reasons they exist. It makes them useful for telling things apart. Unlike doronetics, Mathematics is useful. It distinguishes between things that are and things that are not functions.

At any rate, your very first sentence is bogus. Fix that. No point in the rest of us reading any further.
 
jsfisher said:
Definitions are supposed to limit; that's one of the reasons they exist. It makes them useful for telling things apart.
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Definitions can be expanded from within in order to refine our abilities to use mathematical expressions like numbers, functions etc.

EDIT:

jsfisher said:
Unlike doronetics, Mathematics is useful. It distinguishes between things that are and things that are not functions.
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Unlike Traditional Mathematics that is useful for context-dependent disjoint universes (telling things apart), Organic Mathematics uses also cross-contexts foundation, which enable the linkage among context-dependent mathematical universes. By using cross-contexts foundation, definitions are expanded from within and yet the consistency of the defined things (function, in this case) is kept.

jsfisher said:
At any rate, your very first sentence is bogus. Fix that. No point in the rest of us reading any further.
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EDIT: At any rate, your very first sentence is limited-only. Fix that and please answer to the question in http://www.internationalskeptics.com/forums/showpost.php?p=9717505&postcount=2905.
 
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doronshadmi said:
Definitions can be expanded from within in order to refine our abilities to use mathematical expressions like numbers, functions etc.
Click to expand...

It is true definitions can be expanded and generalized. A generalization of the meaning of square gets us to cubes and hyper-cubes. It can be carried in the other direction, too, to include line segments and points. One expansion on the definition of function gives rise to the term, partial functions. Studying partial functions can lead to new knowledge about...wait for it....wait for it...partial functions.

Great how that works. Too bad doronetics doesn't work that way.

Unlike Traditional Mathematics that is useful for context-dependent disjoint universes, Organic Mathematics uses also cross-contexts foundation, which enable the linkage among context-dependent mathematical universes.
Click to expand...

Now you are just making up terms and tossing them together because you think it all means something. It doesn't. Fix that, then maybe you'd have something to discuss.
 
jsfisher said:
A generalization of the meaning of square gets us to cubes and hyper-cubes.
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A generalization of the meaning of function, enables to deal also with functions that ...wait for it....wait for it.. do not return any output.
 
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doronshadmi said:
A generalization of the meaning of function, enables to deal also with functions that ...wait for it....wait for it.. do not return any output.
Click to expand...

Repeating the same mistake, as you are wont to do, doesn't make it any less of a mistake.
 
jsfisher said:
Repeating the same mistake, as you are wont to do, doesn't make it any less of a mistake.
Click to expand...

Let us take for example the use of Generalization, for example, in http://en.wikipedia.org/wiki/Partial_function
In mathematics, a partial function from X to Y (written as f: X ↛ Y) is a function f: X' → Y, where X' is a subset of X. It generalizes the concept of a function f: X → Y by not forcing f to map every element of X to an element of Y (only some subset X' of X).
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Actually it does not generalizes the concept of a function, it simply ignores some of its possible inputs.

A real generalization, in the case of functions, does not omit any possible input or output. It does not mean that there is a function with no output at all, in case that no possible output can be found.
 
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doronshadmi said:
Let us take for example the use of Generalization, for example, in http://en.wikipedia.org/wiki/Partial_function
Click to expand...

and there were some who doubted your ability to pick up on cues.

Actually it does not generalizes the concept of a function, it simply ignores some of its possible inputs.
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Completely wrong. Partial functions permit a generalized domain. It doesn't ignore anything. It admits there are values for which they are not defined. The partial function over the reals for reciprocal, for example, isn't defined for zero. Looks like a tremendously useful concept to me.

Why does Doronetics exclude the useful?
 
jsfisher said:
Completely wrong. Partial functions permit a generalized domain. It doesn't ignore anything. It admits there are values for which they are not defined. The partial function over the reals for reciprocal, for example, isn't defined for zero. Looks like a tremendously useful concept to me.
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"Not defined", in this case, is equivalent "ignores some values" because of considerations of usability, which is not necessarily equivalent to considerations to get more comprehended (more general) understanding.

jsfisher said:
Why does Doronetics exclude the useful?
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EDIT:

Organic Mathematics does not exclude the useful because it does not reject the usefulness of functions with both input and output, as used by functions or partial functions.

Organic Mathematics simply adds the case of no output as a valid property of (in this case) a function, which enable more comprehended (more general) understanding of infinite sets.

On the contrary Traditional Mathematics unable to do such generalization as long as it gets function as a mathematical expression that must have at least input AND output.

By using Organic Mathematics, one also shows that the pairs' game holds even if a function does not have any output (as seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9717505&postcount=2905).
 
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doronshadmi said:
"Not defined", in this case, is equivalent "ignores some values" because of considerations of usability, which is not necessarily equivalent to considerations to get more comprehended (more general) understanding.
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Why do you insist on anthropomorphizing Mathematics? Functions don't ignore some values. A function has a domain over which it is defined; outside the domain, it is not defined. Anything else would contradict the meaning of 'domain'.

Doronetics is riddled with contradiction. Please stop trying to infect Mathematics with the same nonsense.
 
jsfisher said:
Why do you insist on anthropomorphizing Mathematics? Functions don't ignore some values. A function has a domain over which it is defined; outside the domain, it is not defined. Anything else would contradict the meaning of 'domain'.
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I wrote this about partial functions. Partial function f: X → Y does not necessarily used to map every element of X to an element of Y, or in other words, it is possible that some of the elements of X domain are ignored, as clearly be seen in http://en.wikipedia.org/wiki/Partial_function .

For example:
200px-Partial_function.svg.png


In this case element 1 of domain X, is ignored (or undefined).

So nothing contradicts the meaning of domain, as you wrongly claim about what I wrote about partial functions.

--------------------------------------------
EDIT:

But you see jsfisher we are not talking here about the domain, but about the codomain.

Since according to Traditional Mathematics every function or partial function must have at least input AND output, it can't deal with the type of a function that has an input but no output.

Such a function shows that a given element of the considered domain (an element of X) is beyond the considered codomain (beyond Y).

This is exactly what happens between rooms and visitors in http://www.internationalskeptics.com/forums/showpost.php?p=9717505&postcount=2905.

There is at least one room that is beyond the range of the visitors, even if there is 1-to-1 and onto between the names of the rooms and the names of the visitors.

You can't use claims that are taken from finite set about this case, exactly as you can't do it in the case of the mapping between an infinite set into its proper subset.

Traditional Mathematics knows about mapping between an infinite set into its proper subset, but since its definition of function is restricted to input AND output, it can't deal with the case that there are more rooms than visitors in Hilbert's Hotel even if there is 1-to-1 and onto between the names of the rooms and the names of the visitors, as seen in the pair's game in http://www.internationalskeptics.com/forums/showpost.php?p=9717505&postcount=2905.

By the expanded meaning of the concept of function, a given function has at most one output (unlike the traditional meaning, which according to it, there must be exactly one output to each input ("... with the property that each input is related to exactly one output.", as written in http://en.wikipedia.org/wiki/Function_(mathematics))).
 
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doronshadmi said:
I wrote this about partial functions. Partial function f: X → Y does not necessarily used to map every element of X to an element of Y, or in other words, it is possible that some of the elements of X domain are ignored
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Nope, not ignored. Metaphorical, perhaps, but inappropriate anthropomorphization. You need to be more precise in your word choice. Much of your muddled reasoning is traceable to misuse of vocabulary.
 
doronshadmi said:
I wrote this about partial functions. Partial function f: X → Y does not necessarily used to map every element of X to an element of Y, or in other words, it is possible that some of the elements of X domain are ignored
Click to expand...

I should also mention that there are two meanings for 'domain' in the context of partial functions. The more commonly used meaning is that the domain of the partial function is the same as for the function. That is to say, the domain is the set of elements over which the function is defined.

The reciprocal function is a partial function mapping the reals to the reals. Its domain of the partial function is the reals less the number zero.
 
jsfisher said:
Nope, not ignored. Metaphorical, perhaps, but inappropriate anthropomorphization. You need to be more precise in your word choice. Much of your muddled reasoning is traceable to misuse of vocabulary.
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The name of the game is Observation.

For example:

(mathematician is an agent of function (objective observation)) OR (function is an agent of mathematician (subjective observation)).

The observation types do not exclude each other.

jsfisher said:
I should also mention that there are two meanings for 'domain' in the context of partial functions. The more commonly used meaning is that the domain of the partial function is the same as for the function. That is to say, the domain is the set of elements over which the function is defined.

The reciprocal function is a partial function mapping the reals to the reals. Its domain of the partial function is the reals less the number zero.
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The observation of some element of X is excluded in the case of partial function.

No observation of some element of X is excluded in the case of function.

But once again, the generalization is done by the additional property of no output, such that a function has OR does not have an output (a function has at most one output, which does not exclude the possibility that a function does not have any output (and vise versa)).
 
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doronshadmi said:
The name of the game is Observation.
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The topic of this thread has been the confused and contorted body of misinformation known as Doronetics. The most recent sub-arc to the topic has been your misuse of basic terminology and your insistence definitions in Mathematics adapt to your whim.

Are you now looking to jump to a different sub-arc? You play some strange games.
 
jsfisher said:
The topic of this thread has been the confused and contorted body of misinformation known as Doronetics. The most recent sub-arc to the topic has been your misuse of basic terminology and your insistence definitions in Mathematics adapt to your whim.

Are you now looking to jump to a different sub-arc? You play some strange games.
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Now you are simply try to avoid an open discussion about more comprehended property of the concept of function, which is also function without any output (in addition to function with input AND output).

This kind of discussion style of yours, goes all along this thread. You play only traditional games of the kind that can't go "deeper than primes".
 
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