Proof on how 0 = 1

No, I haven't gone crazy yet ( Or maybe I have and never realised it 😂)

but this is a surprisingly valid proof on how 0 = 1

so we can write

0 = 0+0+0+0+0+0+0+0+0+........ ∞ times

and this can also be expressed as

0 = 1 -1 + 1 -1 +1 - 1 + 1 -1 + 1 -1 +1 - 1 + 1 -1 + 1 -1 +1 - 1 ...... ∞ times

This is valid cause 1 and -1 can be grouped and they result to zero

0= ( 1 - 1 ) + ( 1- 1 ) + ( 1 - 1 ) + ( 1- 1 ) + ( 1 - 1 ) + ( 1- 1 ) + ( 1 - 1 ) + ( 1- 1 ) ...... ∞ times

But this grouping can take place in any way right?

so instead of starting the grouping with the 1st term, why not start with the second term?

0 = 1 + ( -1 + 1) + (-1 +1) +(-1 + 1 ) + ( -1 + 1) + (-1 +1) +(-1 + 1 ) + ( -1 + 1) + (-1 +1) +(-1 + 1 ) ... ∞ times

Now the groups all result to 0

so only thing left is 1

0 = 1

Hence proved !?

If this proof is true, it dismantles entirety of Maths ( not to mention major parts of physics too) < cue evil laugh>

Just think about it if 0 = 1 then one minute later is zero minutes later , which practically means later is now, future is present ( this is where I realise I have definitely gone crazy 😆)

To be completely honest, I agree this is a very controversial proof. even I questioned this proof alot , and these are few points which helped explaine my questions

1) Infinity is a very vague concept in maths, in a way no one really knows what infinity is. It is thought to the concept of something that is unlimited, endless, without bound

2) So when we start grouping from the second terms , you might argue ( like I did) that when you start grouping from the second term, there is always a -1 in the end to cancel out the first +1 which we left out in grouping. This is where infinity plays an important role,

Infinity is something which goes on forever, it has no ends. So even if there is a -1 in the end, as the series go on forever, a +1 follows it immediately. Basically says there is NO END, for us to be sure that there is a -1 to cancel it out.

This is the beauty of ∞. As infinity is an concept which cannot be defined accurately by anyone, it's properties being a big question in the field of maths, it gives such astonishing results in the end

Like I mentioned before, this is a very arguable proof which can be looked upon from many ways and questioned using different points , so discussions are obvi open.

But just think about it, if we can prove 0 = 1 , take something so elemental in maths and prove somethign absolutely crazy , then think about the other million things out there for us to find out.