Wait what? (1+2+3+4+...

[BAndrew]

I am talking about these videos:
https://www.youtube.com/watch?v=w-I6XTVZXww
http://www.youtube.com/watch?v=E-d9mgo8F...e=youtu.be

It suggests that 1+2+3+4+5+... = -1/12.

Spoiler below!

OK, this is ridiculous (I don't care if physicists use it, I only care about it mathematically) and I doubt it's mathematically correct for the following reasons. If someone knows about the subject please inform me, because I think this is some bs. So here we go:

Objection 1:
Proof of first video:
S = 1+2+3+4+5+... is not a valid statement because he is assuming that the sum has a real value and he is doing operations that are true only in R (real number set).
If the sum was infinite then when he says 2S-S it would be ∞-∞ which is undefined and not S.

Objection 2:
Proof of second video:

• What he writes at some point is true for |x|<1 AND NOT x<1 and therefore he can't substitute x= -1 as he later does.
  
• Wikipedia clearly states here that:
  Re(s) > 1 and again he can't substitute x = -1 because Re(-1) = -1<1
  

It gets even worse...

Objection 3:
Another youtuber clearly using a similar method arrives to the conclusion that 1+2+3+4+... = -1




So obviously -1 =/= -1/12

Therefore something is really wrong here.

Objection 4:
I can use the same method to prove that 0 = -1

Let S = 1+2+3+4+...
then 2S = 2+4+6+8+10+...

S = 2S-S = 2+4+6+8+... -(1+2+3+4+...) = 2+3+4+5+6+... = S-1


Hence S = S-1 =>
0 = -1


Good job, Einstein!
Obviously this is not true. If physicists use this then I am really dissapointed and I have lost all the respect I had for them.

Am I right or what?

NOTE: I have changed opinions since I opened this thread. Apparently I rushed on making conclusions.