A mathematical fallacy is a series of steps which is seemingly correct but contains a flawed argument to prove an obvious contradiction or absurdity, such as that 1 = 2. Fallacies differ from simple mistakes in that there is an element of concealment in the presentation of the proof, perhaps hidden by the algebraic notation being used; not only do they lead to an absurd result, they do so in a deliberately deceptive way.[1]

## Example

The following appears to prove that 1 = 2.

Let :
(Multiply both sides by )

(Subtract from both sides)

(Divide both sides by
(Since )

(Divide both sides by )

The deception occurs in the fifth step of the “proof”, the division of both sides of the equation by . As the initial premise is that then that is a division by zero, which is an undefined operation; .

## Bibliography

Maxwell, E. A. (2006). Fallacies in Mathematics. Cambridge University Press.