Why Do These Math Paradoxes Seem to Defy Logic?

[PhysicoRaj]

I'm sure there must be some explanation to why these kind of things appear..

firstly,
consider a=b
ab=b²
a²-ab=a²-b²
a(a-b)=(a+b)(a-b)
a=a+b
since a=b,
b=b+b
1=2 !??


then this one-
(100-100)/(100-100)
=[(10+10)(10-10)/10(10-10)]
=2

Anything has gone wrong?

 

[Mark44]

I'm sure there must be some explanation to why these kind of things appear..

firstly,
consider a=b
ab=b²
a²-ab=a²-b²
a(a-b)=(a+b)(a-b)
a=a+b

Since a = b, then a - b = 0. To get to the line above, you divided by zero, which is never allowed.

since a=b,
b=b+b
1=2 !??


then this one-
(100-100)/(100-100)
=[(10+10)(10-10)/10(10-10)]
=2

Anything has gone wrong?

Here you canceled (10 - 10)/(10 - 10), which is 0/0. You can't do that.