Since a=b, a-b=0 and division by zero is not allowed.
Step 1: a and b > 0
Step 2: a = b
Step 3: a2 = ab
Step 4: a2 - b2 = ab - b2
Step 5: (a + b)(a - b) = b(a - b)
Step 6: (a + b) = b
Step 7: b + b = b
Step 8: 2b = b
Step 9: 2 = 1
This is a flase proof but I wanted to see how many people can find the false step in this.
This is one of the weaker such "proofs".
"Step 1: a and b > 0" -- This step is entirely pointless.
"Step 2: a = b" -- The whole thing is really quite pointless after this.
Substitute this expression into the rest of the "proof".
"Step 3: b^2 = b*b" -- So? Hardly interesting.
"Step 4: b^2 - b^2 = b*b - b^2" -- So? Hardly interesting.
"Step 5: (b + b)(b - b) = b(b - b)" -- or (2b)(0) = b(0) So? Hardly interesting.
Why would you even consider the division step after that?
What did you conclude was wrong with it?
1) Just the division-by-zero problem?
2) The fact that it contains useless and distracting information?
3) The necessity to write the equations in a specific visual way in order for it to be deceiving?
4) That you, a confessed non-mathematician, even for a moment, wondered if people who actually pose as mathematicians might be stumped by such foolishness?
There are quite a few things wrong with it, not just one.
Okay were going down this path now......
Statement: All horses are the same colour.
Proof (by induction): For one horse the statement is true. assume the statement is true for any set of k horses, then consider a set of k+1 horses. then take any two distinct k element subsets and for example. we know that all the horses in the k element subsets are the same colour, so and . this gives . so this prove that for any set of k+1 horse they are the same colour. so by induction all horses are the same colour.
The problem with the proof is that I have shown that being true for k implies also true for k+1 however this proof only works if the k element subsets of a k+1 element set overlap, namely k > 1, so I have shown that if true for 2 also true for 3 ect. but the statement holding for 1 horse does not imply it is true for 2 horses so we have a gap, I must show by other means that the statement is true for 2 horses to complete my proof, but that is impossible.