As your mother said so thought I: “There is no way this is true”

Now, let me disprove the Grandi Series for you (or check on math.stackexchange for more opinions) and let me point out where the Ramanujan Summation falls into the same trap on its assumption … and let’s discuss what this equation could mean instead …

A = 1–1+1–1+1–1⋯

ok, so, then you simply abstract A from one on both sides, right …

1–A = 1-(1–1+1–1+1–1⋯)

on simplifying you find that 1-A =A
But that’s where you go wrong.
I’m not a mathematician, but I find maths very interesting.
However, I haven’t been into the topic of infinity, but applying my mind on this I find that you cannot mix infinite numbers with actual R (real numbers).

Because, your magic trick of hinting in the wrong direction whilst secretly changing the equation is happening right here.

The real equation would be

1–A = A+1

Because you mixed the infinite series with your addition of a (1-) … pardon my poor language … real number … which makes you either make a mistake (which you dub ‘anomaly’, but I think it’s simply incorrect) … or you would have to choose a finite version of your infinite series. Because you add one digit to the series, you’ll also have to add that 1 digit at the end, in order to not instantiate a different (possible) version of your infinite series. That’s like violating Schroedingers Cat. If you observe and influence the instantiated cat as a living one, you must get the living one as per Heisenbergs Dilation Theorem. Thus if you instantiate the even version of the series you should also use the even version in your subsequent formula, you cannot go on with the odd version …

So, that was the magic trick in the formula:
You instantiate an even series on the left, thus gaining 0, or 1–A(A=0).
On the right you go ahead and instantiate an odd series — that’s what your ‘simplification’ does. it takes 1- A[1-(n-1)] …

now, if we consider this by adding the last digit at the end we get the formula as above:
1–A = A+1 … which one can calculate to A=0
which isn’t very spectacular at all …

Now before discussing what we actually are doing if we try and instantiate an infinite series, which I find interesting, but as I said I haven’t read up on the topic before, let me debunk the Ramanujan thing:
B-C = (1–1) + (-2–2) + (3–3) + (-4–4) + (5–5) + (-6–6) ⋯

ok, so you instantiate stopping at 6 … 6 pairs of the Grandi series.

Ok, let me introduce an idea of mine here, that might be already proved or disproved or simply wrong … however, let me assume your A = 1/2 … A was the possibility or the balance or simply the middle of the two extremes compared in the series … it’s kinda like probability possibly.
so, what that tricky Ramanuja does is simply instantiate at 6 and then you get something interesting: 0, -4, -8, -12, -16, …
So you see, basically if you do the same calculation and don’t stop at 6 but at eight the result wouldn’t be -1/12, but -1/16 … if one abstracts that it would be 1+2+3+…+n (stop, instantiation) = -1/(n*2) …

One could then try and prove it but would be proved wrong: eg. for n=2 => 3 = -1/4 … which is wrong …

So, this formula is based on the wrong assumption one can instantiate/mix imaginary infinity with real numbers in an equation. I don’t now maths good enough to know the conventional rules, but I guess one willing might see the point I’m making.

I’d rather propose to think what this could mean instead ….

Could it have to do with probability??? The middle of the extremes of the series … what does it mean then probability in this context? Probability of something becoming true/possible? Is this possibly an indicator wether or not a mathematical construct is feasible/applicable in real life???

Cheers, J