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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.

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# Some help please

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