1. Feb 14, 2004

### repugno

Hello all,

I’m evidently not an expert on Mathematics but I still want to question the consistency of this system. How confident can we really be that there aren’t any big flaws? I have done some research and have found the following paradoxes which I can’t explain.

Assume that
a = b
Multiplying both sides by a,
a² = ab
Subtracting b² from both sides,
a² - b² = ab - b²
Factorizing both sides,
(a + b)(a - b) = b(a - b)
Dividing both sides by (a - b),
a + b = b
Sinse a = b, we substitute and get
b + b = b
So, 2b = b
Devide by b
2 = 1

There is another one...

Assume A + B = C, and assume A = 3 and B = 2.

Multiply both sides of the equation A + B = C by (A + B).

We obtain A² + 2AB + B² = C(A + B)

Rearranging the terms we have

A² + AB - AC = - AB - B² + BC

Factoring out (A + B - C), we have

A(A + B - C) = - B(A + B - C)

Dividing both sides by (A + B - C), that is, dividing by zero, we get A = - B, or A + B = 0, which is evidently absurd.

2. Feb 14, 2004

Staff Emeritus
Assume that
a = b
....
Dividing both sides by (a - b),

Quick now, what is wrong with these two statements?

3. Feb 14, 2004

### repugno

LOL ....…. I realized afterwards that I’m actually dividing by zero . Which explains everything. Maths is saved !!!