Riddle with no answer ?

[miggys]

@sisco

I'm familiar with what you did. I was saying that in a similar fashion we can also get the value to be 0.

However, after thinking about it further, I feel like commutation in an infinite series is not necessarily legal. But after a quick bit of googling I can not find a source either way...

But it's still my favorite series.

[miggys]

(1) We know that a+b = b+a.
(2) We also know that 1+1 = 1 + (+1)
(3) ... and 1-1 = 1 + (-1).

(4) Hence we know that 1+1+1-1-1-1=(+1) + (+1) + (+1) + (-1) + (-1) + (-1)

We can legally swap. Now it's your problem to show that all those properties still apply for a series of infinite length.

What's the due date?

[Idefix82]

What's the due date?

This will take you a while to prove since it's wrong
Your objection to swapping is an absolutely valid one and in fact you are only allowed to swap terms in an absolutely convergent series (see my previous post). This series is not only not absolutely convergent, but it is not convergent at all.

[johnb820]

Here's a simple one.

"This statement is false."

Is that statement in the quotations true or false?

Choosing one or the either, the statement will cause it to contradict its own truth value.