Actually, the fact that you got 2 = 1 is PROOF that your method
to get the solution is NOT mathematically sound. Think about it :)
Why should a process that leads to a contradiction be sound?
This means that somewhere, in some line, you have a false statement,
one that does NOT follow from the previous one. Where? That's for me
to know, and for you to find out... however, I am going to give you a
hint: remember the first line ( a = b )? Given that, what can you say
about a - b ?
Let me leave you with one warning about division. Whenever you have
two numbers x and y, you can always divide x by y and get another
number x/y, ONLY when y is not zero. This is because you don't get a
unique answer when you divide by zero. Since you can't get a solution
when you do that, mathematicians say that division by zero is
undefined.
Actually, the fact that you got 2 = 1 is PROOF that your method
to get the solution is NOT mathematically sound. Think about it :)
Why should a process that leads to a contradiction be sound?
This means that somewhere, in some line, you have a false statement,
one that does NOT follow from the previous one. Where? That's for me
to know, and for you to find out... however, I am going to give you a
hint: remember the first line ( a = b )? Given that, what can you say
about a - b ?
Let me leave you with one warning about division. Whenever you have
two numbers x and y, you can always divide x by y and get another
number x/y, ONLY when y is not zero. This is because you don't get a
unique answer when you divide by zero. Since you can't get a solution
when you do that, mathematicians say that division by zero is
undefined.
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