1=0... to the MAX!!!

[zootm]

right, people are forever posting flawed algebraic proofs to prove 1=0, but they're generally completely obvious. so i'm gonna post some that aren't. these are flawed proofs, but some of them i don't know why, yet (my maths lecturer claims "this week")... so here we go...

(note: these require some knowledge of maths)

1.
consider the series 1, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/5...
from the second term on, each even term is nullified by the term immediately following it (i.e. -1/2 + 1/2 = 0) so the sum of this series-

1 + -1/2 + 1/2 + -1/3 + 1/3 + -1/4 + 1/4 + -1/5... = 1

as 1 is the only term not cancelled by another.

now, if you add brackets, you can get...
(1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) ...

note that
(1/3 - 1/4) = ((4-3)/4.3) = 1/3.4 = 1/12 (. denotes multiplication)
and (1/a - 1/(a+1)) = 1/a(a+1)

so we can rewrite this
1/1.2 + 1/2.3 + 1/3.4 + 1/4.5... = 1 (from before)

but, likewise, we can show that
1/a.(a+1) = -1/a + a/(a+1) <- it works, trust me

and hence that our sequence
1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... = 1/2 - 1/2 + 2/3 - 2/3 + 3/4 - 3/4 ... = 0
(obviously)

so this series =0 and 1, so 1=0.

i'm bored, i'll maybe post the other proofs later. see if you can deal with that one.

[Some1]

and hence that our sequence
1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ... = 1/2 - 1/2 + 2/3 - 2/3 + 3/4 - 3/4 ... = 0
(obviously)

Your flaw (as far as I can see) is that you left the 1 out from the second sequence (i.e. shouldn't it be "1 + 1/2 - 1/2 + 2/3 - 2/3 ..."?). Put the one back in and it works out quite nicely to 1 = 1.

What I don't get is why so many people seem bent on trying to prove something like 1 = 0, or 1 + 1 = 1, or some other pointless thing that would undermine present-day mathematics...do they really gain anything by attempting such a thing? Would they even gain anything if they accomplished it?

[zootm]

Originally posted by Some1
Your flaw (as far as I can see) is that you left the 1 out from the second sequence (i.e. shouldn't it be "1 + 1/2 - 1/2 + 2/3 - 2/3 ..."?). Put the one back in and it works out quite nicely to 1 = 1.

nope, 1 = 1/1, so 1/1 - 1/2 = 1/1.2 = 1/2

the arithmetic is all right, it's the conclusion that's flawed.

[GLewellen]

you sir are an idiot.

[fwgx]

Originally posted by GLewellen
you sir are an idiot.

[Schismx]

The problem with that "proof" is that it is not a periodic series and so you will have a number left over, i.e. 1, (-1/2, 1/2), (-1/3, 1/3)...
(1-1/2)+(1/2-1/3)+...+(1/(n-1)-1/n))+1/n

I hope you understand what I'm getting at...

[zootm]

Originally posted by Schismx
The problem with that "proof" is that it is not a periodic series and so you will have a number left over, i.e. 1, (-1/2, 1/2), (-1/3, 1/3)...
(1-1/2)+(1/2-1/3)+...+(1/(n-1)-1/n))+1/n

I hope you understand what I'm getting at...

yep, that's pretty much it schismx - we haven't gotten to the real nuts and bolts of getting round it yet, but to the best of my knowledge that's why you're just plain not allowed to do that sort of thing with infinite series. or calculus (which is why a whole lot of calculations by physicists end up being wrong - lack of rigour )