The final solution to Russell’s paradox: The Egyptian method ends the challenge to mathematical foundations in the twentieth century

One of the most beautiful things in this world is mathematical paradoxes, and when there is a paradox, you will find with it a philosophy, and every philosophy has a logic, and every logic has a standard, and every standard has properties, and every property has a function, and every function has limits, and every limit has a scope, and every scope is linked to the essence and essence of things, and depends on the limits of time and space. (Space-Time) In my article, I explain the way to explain this paradox in the authentic Egyptian way, which explains the paradox on several criteria.

(mathematically – logically – fundamentally)

Mathematical logic in the Egyptian way

Suppose that there is a set W, which is the set of positive integers

W = {1, 2, 3, 4, 5, 6, 7, 8, ...........}

It is a unique group, and when you look at this group, it is logical that W will not belong to itself

We reformulate the set W into two inner sets, odd and even

W= {{ 1, 3, 5, ……}, { 2, 4, 6, …….}}

Also, you will find that W does not belong to itself

We rephrase again by removing the two groups and adding symbols for the place of each group to become W

W = { O , E }

O is the set of odd numbers

E is the set of even numbers

If you consider O and E to be sets, then

O is part of W and

E is part of W

But if O and E are considered just two symbols, the standard will differ to become O and E belong to W

You can write W in another way after taking 2 common factors from the set of even numbers

W ={{ 1 , 3 , 5 , ……} , 2 { 1 , 2 , 3 , 4 , ……}}

W = { O , 2 W }

If you consider that the term in front of you is two sets within a set W, then this is mathematically correct. However, if you consider that it is just two symbols, it is not permissible to repeat the element within the set, so W is written in this way.

W = { { 2 , 5 , 8 ,11 , …..} , { 1 , 2 , 3 , 4 , 5 , …..}}

W = { O + W , W }

When elements of two sets are combined, a new set is produced, so. O + W = Y

Then W = { Y , W }

So we find

Here branches of group W appear within the same group and are defined as follows

1- An internal virtual group

2- 2- Synthetic inner group Y

3- An internal, external element

4- Internal synthetic element

Conclusion

W is a set that is part of itself

W is an element of itself

W is an inner set of the parent set W

W is an element of an inner set of the parent set



Thank you to Russell. I was creative with this paradox, and the explanation of the solution to the Barber’s Paradox will be in my next article. Greetings to all readers. This article is part of my research. I hope you like it.