how can we prove 1+1=0?

Question

their is a logical solution but i forgot it.

Answer 1

The classic puzzle is posed as follows:

let a = b by definition

then:

a^2 = ab [multiply by a, both sides]
a^2 - b^2 = ab - b^2 [subtracting b^2]
(a+b)(a-b) = b(a-b) [factoring both sides]
(a+b) = b [ cancelling (a-b)]

but since we defined a = b, we can substitute:

a+a = a or
2a = a

i.e., 2 = 1 !!!!

This would appear to be a proof that 2 = 1, which of course is a false statement. The question is then, "What went wrong with the proof?" On the face of it, the algebraic manipulations appear to be very basic and without problems!

The logical failure is that we "cancelled" (a-b) on both sides. This, however, is just a sloppy way of saying that we divided both sides of the equation by (a-b) and then factored out the (a-b)/(a-b) as a 1 and removed those symbols. Thats what it means to "cancel". This is an illegal operation, though, because we defined a=b at the beginning, which means that a-b=0 !!

By dividing by zero, the terms become undefined and the rest of the algebra is nonsense. In effect, after that line, all that we are writing is "infinity equals infinity" which is just mathematical gobbledegook.

I hope this helps with what you were curious about. In fact, you cannot "prove" that 1+1=0 because the definitions of "1", "0", "+" and "=" cannot be put together so that 1+1=0 is a true statement. Any logical system which permits the derrivation of contradictory statements is termed "inconsistant".

PS - kudos go to "angy" above, who understood this concept. All I did was to elaborate.

Answer 2

1+1=2

Answer 3

certain. Crappy good judgment. branch is defined as 'the fashion of circumstances one volume must be subtracted from yet another'. in case you commence with a million (or the different volume), and subtract 0, you could proceed doing that a limiteless style of circumstances. So 'infinity' isn't a volume and to imagine that you'll be able to subtract some thing from infinity is pretend. a million/0 = ? is a real statement. a million/0 =?-a isn't in basic terms unfaithful, that's invalid till a=0 0/a million = 0 is likewise authentic, yet 0/a million = 0-b is basically authentic if b=0 In different words you're making use of computaional practice to issues which aren't any further numbers. 0 isn't a 'volume' by making use of definition, ? isn't a volume because it merely ability 'no end'. in case you should educate that team spirit is an analogous as 0, then you extremely ought to have proved that God does no longer exist (even with the indisputable fact that it truly is totally yet another argument.)

Answer 4

You can prove 1=0 or 1=2, but I don't think you can prove 1+1=0.

Actually, if you can prove that 1=0 then it is easy to prove that 1+1=0, because:
If 1=0, then 1+1=0.

Here is the proof

http://www.pen.k12.va.us/Div/Winchester/jhhs/math/humor/onezero2.html

Answer 5

did you mean 1-1=0 or 1+-1=0?

Answer 6

Better yet, how can we prove that 0 +0 = 1 ?

Answer 7

I don't know but I have a friend who can prove that 1=0 and that math is a complete lie.

Answer 8

their or there ? if both are same 1+1=0 hence proved .

Answer 9

Simple:

a glass that is half full is also half empty. Hence
1/2 full = 1/2 empty
you multiply by 1/2 and you arrive at full = empty

now: one glass of water equals 1

There you go, silly boy

Answer 10

1/infinity+1/infinity=0+0=0
Hence proven