Originally Posted By: CivicFan
If
a = b
Then
axa = axb
axa + axa = axa + axb
axa + axa - 2axb = axa + axb - 2axb
2axa - 2axb = axa - axb
2X(axa - axb) = 1x(axa - axb)
Therefore
2 = 1
Your steps are wrong, you mis-carried a term in your simplification/obfuscation...and you need to get rid of all the "x"...this is algebra, the "x" is implicit...so, it should read:
a = b
Then
multiplying by a
aa = ab
adding the term aa to both sides
aa + aa = aa + ab
subtracting 2ab from both sides
aa + aa - 2ab = aa + ab - 2ab
so far, so good, but now you combine terms:
2aa - 2ab = aa - ab
and you factor
2(aa - ab) = 1(aa - ab)
or, since we know aa = ab from above
2x(0) = 1x(0) which is true, both sides of the equation are
zero.
But, you can't divide both sides by zero!
So, it does not follw that 2=1...the only thing you've proved is that two different numbers times zero equal zero...once you have 0=0 it becomes meaningless at that point...
Which is what the other guys said while I was away from the computer...but hey, I went step by step...
Cheers,