Question:
can anybody prove to me that 1=0?
seekinghelp
19 years ago
proof to me that 1=0?
Five answers:
nate
19 years ago
this is a common "proof" that is often bandied about, even though it's wrong.



Let a=b.



multiply by a:

a^2 = ab



subtract b^2:

a^2 - b^2 = ab - b^2



factor both sides:

(a+b)(a-b) = (a-b)b



cancel (a-b)

(a+b) = b



substitute a=b from the first step:

2b = b



divide by b:

2=1



subtract 1 from both sides

1=0





fortunately sanity is saved when you realize that the step where you cancel (b-a) from both sides is actually dividing by zero, since you specify beforehand that b=a. this is not so much a proof as a mathematical fallacy. see the link below for another, more complicated version of the same thing.
aditsu
19 years ago
I asked the same thing, and the best answer I got was:

1 = sqrt(1) = sqrt(-1*-1) = sqrt(-1)*sqrt(-1)=i*i = i^2 = -1

So 1=-1; just add 1 and divide by 2 and you get 1=0
Grouchy Dude
19 years ago
No they can't, because 1 does not equal 0.
dougs249
19 years ago
it does not
angelbaby
19 years ago
I can't, but they can.


This content was originally posted on Y! Answers, a Q&A website that shut down in 2021.
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