Actual infinity (Definition). Continuing the theme

Actual infinity (Definition).

Actual infinity is some integer, (k) which has the following properties,

  The number of (k), increases in magnitude. To what value is undefined. But there is a limit increase this number, although this limit, as some specific number, is determinable.

These three conditions represent actual infinity.

The latter condition determines the existence of actual infinity.

For example:

   Actual infinity is an integer (k) where, for any (n)

To prove there is a limit growth in the number (k)

 

It suffices to prove

This was proved in our (dxdy), but did not answer the question of the legitimacy of the comparison of formulas.

definition

contradicts the theory of sets. Also contrary to theory, and gross units, and simply contradicts the definition of infinity as an endless number of items.
And talk about the power of a set in this case is not necessary, it is not the number of items. This is the limit of growth of magnitude (k). And this limit is determinable. Although it exists.
What does the new, such a definition of actual infinity?
Unfinished debate on the fifth page, will be continued the following:

This equality is not true, because the desire for infinity and reaching infinity, it is not the same thing.

These two characters are not identical.
But the new equality, where the number (k) is an actual infinity is true:

  It follows

which means that the number of prime (k). After the prime (p_k), there is no prime numbers. Not in the sense, of course, that they do not, do not have their number is infinite. After a number (k) the gap between primes is infinite, the number (k).
Let me remind you. The number of (k) is increasing in magnitude. But there is a limit increase this number. And this limit, as some specific number, is determinable. Although it exists.

Still, I'm right, as it were, and who would not seek to infinity always

  

    Sergey Sitnikov