This classic clip “proves” how 25/5 = 14, and does it three different ways. Maths is a powerful method for providing proof – but we need to be careful that each step is based on correct assumptions.

One of the most well known fake proofs is as follows:

let a = b

Then a^{2} = ab

a^{2} – b^{2} = ab – b^{2}

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

a+b = b (divide by a-b )

b+b = b (as a = b)

2b = b

2 = 1

Can you spot the step that causes the proof to be incorrect?

Another well known maths problem that appears to prove the impossible is the following:

This was created by magician Paul Curry – and is called Curry’s Paradox. You can work out the areas of all the 4 different coloured shapes on both triangles, and yet by simply rearranging them you created a different area.

A third “proof” shows that -1 = 1:

Let a = b = -1

a^{2} = b^{2}

2a^{2} = 2b^{2}

a^{2} = 2b^{2} – a^{2}

a = √(2b^{2} – a^{2})

a = √(2(-1)^{2} – (-1)^{2})

a = √(1)

-1 = 1

And finally a proof that 1= 0. This last proof was used by Italian mathematician Guido Ubaldus as an example of a proof of God because it showed how something could appear from nothing.

0 = 0 + 0 + 0 + 0 ……

0 = (1-1) + (1-1) + (1-1) + (1-1) ……

0 = 1-1+1-1+1….

0 = 1 + (-1+1 ) + (-1+1) + ….

0 = 1

So, maths is a powerful tool for convincing people of an argument – but you always need to make sure that the maths is accurate! If you want to see the problems in the above proofs, highlight below (explanation in white text):

1) We divide by (a-b) in the 5th line. As a = b, then (a-b) = 0. We can’t divide by zero!

2) Neither of the “triangles” are in fact triangles – the hypotenuse is not actually straight. This discrepancy allows for the apparent paradox.

3) In the second to last line we square root 1, but this has 2 possible answers, 1 or -1. As a is already defined as a = -1 then there is no contradiction.

4) This is very similar to the Cesaro Summation problem which exercised mathematicians for centuries. The infinite summation of 0 + 0 + 0 + 0 … is not the same as the infinite summation 1 – 1 + 1 – 1 + 1 ….

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December 1, 2013 at 10:15 am

tPenguinLTGReblogged this on `The Penguin' says… and commented:

I always loved doing tricks like these on my friends!

July 3, 2016 at 9:29 am

zodituThe last one is inconsistent for me because… When does (1-1) transforms into 1?

1 = 0 is not a well formulated paradox because the base of the 0 + 0 + 0 proof affirms than any negative/positive operation term has to be a negative/positive operation of a pair members count. This means:

0 = 1-1

0 = 1-1+1-1

This italian dude is doing something weird that cannot be done even with algebraic factorization here:

0 = (1-1) + 1… Why is there (+1) ? This is contradictory to his first affirmation which says: 0 + 0 + 0 = (1-1) + (1-1) + (1-1)

Is inconsistent, not true.

And it’s not only 1, it may be 2, 3, 4.56, 0.99999 where (0.9999 – 0.9999) = 0… That includes the 0 himself where 0 = (0-0) or 0 = (0+0)

So as a summary: It doesn’t says that from nothing can appear something. It strictly affirms that from nothing there “appears” to be something but you discover that this “something” is really the “nothing”. Because 1 = 0 is not true, it’s something that really doesn’t exists cause 0 = 1 is fake and 0 = 1 is really 0 = 0. This is just an illusion, just as god. It’s just an illusion, imagination. If you use the religion fact this will be: “0 = 1 can be true if you believe it, but the truth is 0 = 0, and 1 is not something but nothing that only exists if you believe it”.