@@neuralwarp Well, I think some of the mathematicians don't even want to understand Infinity.... and that's a issue for why Ramanujan summation is considered incorrect. And there are so call undefined/indeterminate forms. In short: if we define Infinity as unbounded, than any condition imposed on Infinity it is also a boundary. So, classical logic can't be applied on Infinity. Only infinite value logic would be suitable. Unfortunately as finite beings, we wouldn't be able to understand infinite value logic, so we will use finite (at least 4 value logic) as a bad model, but still better than classical logic. In short when Infinity is involved, classical logic works only in special cases. I develop my Infinity definitions since I was a child and bother my parents with this question: what is Infinity? Still, I have no complete and coherent definition. But I understand that Infinity is unbounded and it is the mother of all veridical paradoxes. Anyway, thank you for you answer.
I joined half way through the premiere - at Method 1 - enjoyed that
If Ramanujan summation is incorrect, then why it has real applications in physics (Casimir effect)?
Physics only needs correct solutions. In Maths, how you get there is more important.
@@neuralwarp Well, I think some of the mathematicians don't even want to understand Infinity.... and that's a issue for why Ramanujan summation is considered incorrect. And there are so call undefined/indeterminate forms.
In short: if we define Infinity as unbounded, than any condition imposed on Infinity it is also a boundary. So, classical logic can't be applied on Infinity. Only infinite value logic would be suitable. Unfortunately as finite beings, we wouldn't be able to understand infinite value logic, so we will use finite (at least 4 value logic) as a bad model, but still better than classical logic.
In short when Infinity is involved, classical logic works only in special cases.
I develop my Infinity definitions since I was a child and bother my parents with this question: what is Infinity? Still, I have no complete and coherent definition. But I understand that Infinity is unbounded and it is the mother of all veridical paradoxes.
Anyway, thank you for you answer.
Haven't we just done this one? A repetitive pattern of videos.
Σ (2n + 1) / 4^n = Σ (2n + 1) x^n for x = 1/4 and n = 0, 1, 2, 3, ...
Σ (2n + 1) x^n = Σ (-1 + 2 + 2x + 2x² + 2x³ + ...) x^n = (-1 + 2 + 2x + 2x² + 2x³ + ...) 1 / (1 - x)
=[ -1 + 2 / (1 - x) ] / (1 - x) = (1 + x) / (1 - x)² = 20/9 for x = 1/4