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The Magic Cafe Forum Index » » Puzzle me this... » » 1 = 0 (0 Likes) Printer Friendly Version

James F
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A proof that 1=0

a=b

a-b+b=b (statment)

a-b+b/a-b = b/a-b (divide both sides of the equation by a-b)

1+b/a-b = b/a-b (simplify equation)

1=0 (subtract b/a-b from both sides)


Keep in mind this is a false proof. This one is pretty basic but still fun to look at. Can anyone spot the error?

James
Stephen Buxton
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If a=b, then a-b = 0, so dividing the equation by by a-b is the same as dividing by zero.
If you put an infinite number of apes in front of an infinite number of computers, you get a pretty good idea of what internet chat rooms can be like
James F
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Yeah you got it.

Alright, that one was a little too easy. This one is a little hard to follow unless it is written properly on paper. Ill do my best though. It uses complex numbers. I will use the term 'sqrt' to mean a square root sign. I don't think anyone will get this one that fast. don't ruin it by looking it up, try to find the error yourself.

Proof that 1=2

-1/1 = 1/-1 (statement)

sqrt-1/1 = sqrt1/-1 (square root both sides)

sqrt-1/sqrt1 = sqrt1/sqrt-1 (simplify)

i/1 = 1/i (change sqrt-1 intto 'i')

i/2 = 1/2i (divide both sides of the equation by 2)

i/2 + 3/2i = 1/2i + 3/2i (add 3/2i to both sides of the equation)

i(i/2 + 3/2i) = i(1/2i + 3/2i) (multiply both sides by i)

i^2/2 + 3i/2i = i/2i + 3i/2i (distribute)

-1/2 + 3/2 = 2 + 3/2 (simplify)

2/2 = 4/2 (simplify)

1 = 2 (simplify)
mike paris
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A little too easy? are you kidding,i just got to learning adding up my fingers and toes, (then I had to recount)he he ,mike
Stephen Buxton
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I don't think that this part is correct:

2 + 3/2 simplifies to 4/2 ???

I think that should be 1/2 + 3/2
If you put an infinite number of apes in front of an infinite number of computers, you get a pretty good idea of what internet chat rooms can be like
James F
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Atlanta
1097 Posts

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Stephen,

haha! You are exactly right. (I was copying this from a piece of paper I have and made a typo) I actually copied the simplification down wrong.

i/2i + 3i/2i (4th line from the bottom)

Would simplify to 1/2 + 3/2 which is equal to 4/2 which = 2.
Thanks for pointing that out.

James
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