I read the theory/math/logic thread but might as well post here that one should never forget that buddhism is a meditative path. 
The views and conclusions regarding self & not-self all stem from advanced meditators who have all been around since the beginning of time.
The conclusions are based on their meditative experiences or spiritual paths, be they eternalists, partial-eternalists or annihilationists.
All their views are valid since they have no access to The Buddha’s Dhamma.
Two types av eternalists:
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Those beyond the sensual heavens with a more coherent self since they can’t remember their previous existences and have no clue of impermanence in the realm they reside.
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Meditators who recollects previous existences on earth, in various heavens and so on and who come to the conclusion that this eternal wandering of death and rebirth will never come to an end.
Annihilationists:
All 7 types of annihilantioists has a notion of a self and 6 of them believe in rebirth.
Only the materialist denies rebirth, the remaining 6 annihilationists are ascetics and brahmins who are on a spiritual path, believe in rebirth and do not deny a self.
If these ascetic annihilationists happen to be practicing self-mortification in order to reach deep states of concentration, they see the body and world where they practice as not-self/non-existence.
They couldn’t care less if their body, which they see as not-self, would die.
When they finally die it is not, in their view, the same that takes rebirth but another.
The one dying has nothing to do with the one taking rebirth.
Hence the doctrine of annihilation.
The partial-eternalists are pretty much the same as the annihilationists, but might practice in a different way.
So in their own respective spheres of experiences the eternalists, partial-eternalists and annihilationists can be said to be correct.
They are not making up these various conclusions out of the blue, rather there is a certain logic as to why they see things the way they do.
Only with The Buddha’s superior insights can one begin to realise how they misapprehend their mediatative experiences and the goal of their practice.

So the doctrine of ”no self at all” is not only completely alien to eternalists, partial-eternalists or annihilationists it is also a completely absurd idea according to The Buddha himself:
In the Attakārīsutta AN 6.38, when a brahmin told him that “Venerable Gotama, I am one of such a doctrine, of such a view: ‘There is no self-doer, there is no other-doer.’”, the Buddha replied “I have not, brahman, seen or heard such a doctrine, such a view. How, indeed, could one—moving forward by himself, moving back by himself —say: ‘There is no self-doer, there is no other-doer’?
- Making it crystal clear that the doctrine of ”there is no self at all” is not what The Buddha taught.
And to further elucidate this please read the following:
Acelakassapasutta:
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“Kassapa, if one thinks, ‘The one who acts is the same as the one who experiences the result,’ then one asserts with reference to one existing from the beginning: ‘Suffering is created by oneself.’ When one asserts thus, this amounts to eternalism.
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But, Kassapa, if one thinks, ‘The one who acts is one, the one who experiences the result is another,’ then one asserts with reference to one stricken by feeling: ‘Suffering is created by another.’ When one asserts thus, this amounts to annihilationism.
Without veering towards either of these extremes, the Tathagata teaches the Dhamma by the middle: - SN 12.17
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Dhamma by the middle is not ”there is no self at all”, which is an extreme doctrine refuted in AN 6.38.
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Dhamma by the middle is the following, where we keep in mind how eternalists, partial-eternalists and annihilationists view things:
Ānandasutta SN 44.10
“If, Ānanda, when I was asked by the wanderer Vacchagotta, ‘Is there a self?’ I had answered, ‘There is a self,’ this would have been siding with those ascetics and brahmins who are eternalists.
And if, when I was asked by him, ‘Is there no self?’ I had answered, ‘There is no self,’ this would have been siding with those ascetics and brahmins who are annihilationists.
“If, Ānanda, when I was asked by the wanderer Vacchagotta, ‘Is there a self?’ I had answered, ‘There is a self,’ would this have been consistent on my part with the arising of the knowledge that ‘all phenomena are nonself’?”
“No, venerable sir.”
“And if, when I was asked by him, ‘Is there no self?’ I had answered, ‘There is no self,’ the wanderer Vacchagotta, already confused, would have fallen into even greater confusion, thinking, ‘It seems that the self I formerly had does not exist now.’”
- And this great confusion mentioned in the end of Ānandasutta SN 44.10 is of course the following from MN 2:
‘Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what did I become in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I become in the future?’ Or else he is inwardly perplexed about the present thus: ‘Am I? Am I not? What am I? How am I? Where has this being come from? Where will it go?’
“When he attends unwisely in this way, the view ‘no self exists for me’ arises in him as true and established;
- ‘natthi me attā’ti vā assa saccato thetato diṭṭhi uppajjati;
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- “The view arises for him, truly and correctly, that ‘there is no self’ (natthi me attā).” - MN2
Eternalists, partial-eternalists and annihilationists would never come to this wrong conclusion/doctrine mentioned in MN 2, since they all still hold to a notion of a self in some form or another.
Please remember how annihilationists view rebirth.
And this wrong and confused doctrine found in MN 2 is clearly refuted in Attakārīsutta AN 6.38:
6.38. The Self-Doer
Then a certain brahman approached the Blessed One; having approached the Blessed One, he exchanged friendly greetings. After pleasant conversation had passed between them, he sat to one side. Having sat to one side, the brahman spoke to the Blessed One thus:
“Venerable Gotama, I am one of such a doctrine, of such a view: ‘There is no self-doer, there is no other-doer.’”
“I have not, brahman, seen or heard such a doctrine, such a view. How, indeed, could one—moving forward by himself, moving back by himself —say: ‘There is no self-doer, there is no other-doer’?
What do you think, brahmin, is there an element or principle of initiating or beginning an action?”
“Just so, Venerable Sir.”
“When there is an element of initiating, are initiating beings clearly discerned?”
“Just so, Venerable Sir.”
“So, brahmin, when there is the element of initiating, initiating beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer.
“What do you think, brahmin, is there an element of exertion … is there an element of effort … is there an element of steadfastness … is there an element of persistence … is there an element of endeavoring?”
“Just so, Venerable Sir.”
“When there is an element of endeavoring, are endeavoring beings clearly discerned?”
“Just so, Venerable Sir.”
“So, brahmin, when there is the element of endeavoring, endeavoring beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer. I have not, brahmin, seen or heard such a doctrine, such a view as yours. How, indeed, could one—moving forward by himself, moving back by himself—say ‘There is no self-doer, there is no other-doer’?”
“Superb, Venerable Gotama! Superb, Venerable Gotama! Venerable Gotama has made the Dhamma clear in many ways, as though he were turning upright what had been turned upside down, revealing what had been concealed, showing the way to one who was lost, or holding up a lamp in the dark: ‘Those who have eyes see forms!’ Just so, the Venerable Gotama has illuminated the Dhamma in various ways. I go to Venerable Gotama as refuge, and to the Dhamma, and to the assembly of monks. From this day, for as long as I am endowed with breath, let Venerable Gotama remember me as a lay follower who has gone to him for refuge.”
If, Ānanda, when I was asked by the wanderer Vacchagotta, ‘Is there a self?’ I had answered, ‘There is a self,’ would this have been consistent on my part with the arising of the knowledge that ‘all phenomena are nonself’?”
With a deeper, more developed and nuanced approach to:
- Anicca, Dukkha & Anatta
- Dependent Origination.
- Death/Rebirth
It is impossible to claim: ”there is no self at all”.
