Gödel’s incompleteness theorems

Gödel’s incompleteness theorems. In this video, we are going to discuss a simple example how any set of axioms give a contradiction.
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Maksym Zubkov

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Please watch: "Real Projective Space, n=1"
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[eliasarguello]

My favorite topics are category theory, abstract algebra, and mathematical logic (specifically proof theory). Love your channel by the way!

[jamestagge]

Russell’s paradox is piffle. It is very resolvable. In it, the two sets of men upon which the paradoxical function depends, those who shave (instead of haircuts) themselves and those who do not are defined by three identical criteria and one peculiar to each set which is the deciding factor in their separation. For the former, they are men, they live in town and they must be beardless. These being the same, they do “not” act to separate the men in the town into the two distinct sets, again, upon which the paradox depends, only the relationship to shaving of each does so. The barber’s sign which instructs that he shaves only those men who do not shave themselves is suggested to apply to him as well, but this could not be if the definition of the paradox were to remain true to the logic by which the first two sets of men were defined as such. The barber also shares the three criteria by which the first two sets of men are defined, that they are men, that they live in town and that they must be shaved. Therefore, he by definition must be a member of a third set of men by virtue of his own unique relationship to shaving (as with the other two sets of men), that he shaves others. Deny this and you deny the means of the definition of the first two sets of men and the paradox fails. Accept it and the paradox fails. This is because it is not a paradox. There are no paradoxes which are not formulated by sophistry, abuses of the architecture of language and the logic which allows that they (the paradoxes) might be formulated at all in the first place.

[rounaksinha]

I am Radhadas(ROUNAK SINHA)
I am from India, the land of Ramanujan.
I am 16 years old and study in 12 th grade.
My favourite topic is partition and complex analysis.

[bogdansofalca]

Hi. Why does the barber have to be unique? (i.e. why can't there exist more barbers)

[daaa]

Doesn't Godel theorem require peano axioms to hold?

[mousiki]

Why can't the barber go to another village and cut his hair with that village's barber?