Some comments on information theory

[ark]

The infinite continuation of a specific sum series. I am assuming the exclamation point is a typo. I could be wrong?

What does that mean? Is it mathematics? Or is it a poetic expression? If it is mathematics, I do not know such a concept as "infinite continuation". What would it mean that two "infinite continuations are equal? Is 1+1+1 ... = 1+2+3.... true? When two differently looking infinite continuations are supposed to be related by the "=" symbol?

 

[christx11]

What does that mean? Is it mathematics? Or is it a poetic expression? If it is mathematics, I do not know such a concept as "infinite continuation". What would it mean that two "infinite continuations are equal? Is 1+1+1 ... = 1+2+3.... true? When two differently looking infinite continuations are supposed to be related by the "=" symbol?

I understand what you are saying. I just don't understand where you are saying I am doing what you refer to.

Are you saying for example:

x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...

Are you saying the right hand side of the above ( the sum series of all natural numbers),
Are you saying the right hand side cannot be re-written as two infinite sum series as the evens plus the odds?

As in:

x = ( 2 + 4 + 6 + 8 + 10 + 12 +14 + ... ) + ( 1 + 3 + 5 + 7 + 9 +11 +13 + ... )

Are you saying that the sum of the odds plus the sum of the evens is not the sum of all natural numbers?

 

[ark]

I am saying that I do not know the concept of "infinite sum series". Please define the concept for me. Or give a link. I can't find it online.

 

[ark]

I am saying that I do not know the concept of "infinite sum series". Please define the concept for me. Or give a link. I can't find it online.

Or, more exactly, what the equal sign "=" between two such formal expressions means for you.
In your case both sides are divergent. They produce both infinity. What do you mean by the fact that the two infinities are "equal"?

 

[ark]

Or, more exactly, what the equal sign "=" between two such formal expressions means for you.
In your case both sides are divergent. They produce both infinity. What do you mean by the fact that the two infinities are "equal"?

You probably mean (I am guessing), that with an appropriate procedure on the right hand side (infinite product) you can recover the elements of the left hand side one-by-one? Is that what you mean? Not only "elements" but also partial sums. Is this the case?