I would like some input into this question I need to solve.
From my logic: $a = 1$. we get this from $1=2$ ($a=2a$). It appears $b = 0$. because $a = a + b$ ($1=1+0$).
so in the original statement $a = b$ - meaning both $a$ and $b$ are $0$. So all operations would be zero.
My answer would then be : d) Multiplication by zero is meaningless.
Is this correct?
Let a = b
Then a * b = b^2
And, a * a – a * b = a^2 – b^2
So, a * (a – b) = (a + b) * (a – b)
Or, a = a + b
Or a = 2a
So, 1 = 2
a) 1 and 2 are close so what is the big deal?
b) The Laplace transform of 1 and 2 are identical
c) Division by zero is meaningless.
d) Multiplication by zero is meaningless.
e) The reasoning is absurd because no units are specified.
Multiplication by zero is not meaningless. Division by zero is. The error occurred when going from $$a(a-b)=(a+b)(a-b)$$ to $$a=a+b,$$ since we can only conclude this if $a-b\ne 0,$ but by assumption $a=b,$ so $a-b=0$. So, while it's certainly true that $a(a-b)=(a+b)(a-b)$--after all, $0=0$)--we can't conclude that $a=a+b$.
Another problem occurred in going from $a=2a$ to $1=2$. The only number that is twice itself is $0$, so if $a=2a$, then $a=0$, and we cannot divide by it.