ong>Step-by-step explanation:

It has been said that if you assume a falsehood, you can prove anything.

But i can't prove that!

But most if not all mathematical fallacies can be turned to 'prove 1=2

I can see two CLASSES of fallacies here

One is

If F(x) =F(y) then x=y

This is true only if the mapping is one to one, if it is not, then the implicit inverse mapping F-1(F(y)) is not unique, but the non uniqueness may be hidden by convention,

Eg F: square F-1: SQRT , convention: sqrt(4) MEANS postive sqrt

Application: x^2= (-x)^2, x= -x add 3X 4x=2x divide by 2x, 2=1

Other examples

sin, differentiate, x^0, x*0, 1^x, x+ infinity, x* infinity

Linked to the above is the false assumption that

F(G(x)) = G(F(x))

Examples i have seen include

For F , G ( when it is false)

Multiply , square root ( negative numbers)

Divide, square root ( ditto)

Sum , INTEGRATE ( over the same variable)

The reason that the fallacies are credible, is that we are persuaded that what we find to be commonly true is universilly true, and the fallicy is hidden amongst complicated but correct stuff.

Other fallacies below are based on optical illusion, linguistic ambiguity, logical failures etc.

Tq