I suppose it was too much to ask , for an American to come up up with an imaginative thread
Mathematics seems to a subject of some mystery, for many folks, so Let_Us contribute this little conundrum for your contemplation
Let's start wit a fact. WE KNOW it's a fact, because We MADE it a fact! A = B
Now, IF A = B, then, IF we do the same thing to A, as we do to B, then they OUGHT to remain equal.
A X A = B X A, which equals A squared = AB
Now, IF we subtract B squared from both sides, we end up with A squared - B squared = AB - B squared
BOTH sides of this equation have factors (factors = integral parts, that, when combined, will equal the original thing). In this case A squared - B squared has 2 factors. (A + B) & (A - B). (A + B) X (A - B) = A squared - B squared. And AB - B squared also has 2 factors (A - B) & (B). (A - B) X (B) = AB - B squared. So, NOW we have
(A + B) X (A - B) = (A - B) X (B)
Now, since both halves of this equality have one factor in common, we can divide each half of the equation by that factor (A - B), thus eliminating that factor from each side of the equation, and it will STILL remain equal. Thus
(A + B) X (A - B) = (A - B) X (B) (A - B) (A - B)
Which comes out to be (A + B) = (B)
Now, since we SET "A" to be = to "B", in our initial statement of fact, we can substitute "B" for "A" because they ARE equal. Which leaves us with
(B + B) = (B)
Therefore, (2B) = (B)! And, once again, we have a common factor that can be removed by dividing both sides of the equation by THAT factor. In THIS case (B). Thus
2B = (B) (B) (B)
Which comes out to be (2) = (1)
Now I ASSURE YOU I've followed mathematical procedure scrupulously and correctly, to arrive at our answer. There's ABSOLUTELY NOTHING WRONG, with the mathematics, used above. But this EXACT "proof" was the cause of the promulgation of a NEW Axiom, in the field of mathematics. The reason for a NEW rule being created. Would ANY of you care to explain to me HOW 2 can equal 1? And WHAT the NEW rule was, that was created, as a consequence of this proof?
I'd appreciate reading what you have to say. And I'll give a Gold Star to the first one to explain this CORRECTLY, to me.
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Mathematics seems to a subject of some mystery, for many folks, so Let_Us contribute this little conundrum for your contemplation
Let's start wit a fact. WE KNOW it's a fact, because We MADE it a fact! A = B
Now, IF A = B, then, IF we do the same thing to A, as we do to B, then they OUGHT to remain equal.
A X A = B X A, which equals A squared = AB
Now, IF we subtract B squared from both sides, we end up with A squared - B squared = AB - B squared
BOTH sides of this equation have factors (factors = integral parts, that, when combined, will equal the original thing). In this case A squared - B squared has 2 factors. (A + B) & (A - B). (A + B) X (A - B) = A squared - B squared. And AB - B squared also has 2 factors (A - B) & (B). (A - B) X (B) = AB - B squared. So, NOW we have
(A + B) X (A - B) = (A - B) X (B)
Now, since both halves of this equality have one factor in common, we can divide each half of the equation by that factor (A - B), thus eliminating that factor from each side of the equation, and it will STILL remain equal. Thus
(A + B) X (A - B) = (A - B) X (B)
(A - B) (A - B)
Which comes out to be (A + B) = (B)
Now, since we SET "A" to be = to "B", in our initial statement of fact, we can substitute "B" for "A" because they ARE equal. Which leaves us with
(B + B) = (B)
Therefore, (2B) = (B)! And, once again, we have a common factor that can be removed by dividing both sides of the equation by THAT factor. In THIS case (B). Thus
2B = (B)
(B) (B)
Which comes out to be (2) = (1)
Now I ASSURE YOU I've followed mathematical procedure scrupulously and correctly, to arrive at our answer. There's ABSOLUTELY NOTHING WRONG, with the mathematics, used above. But this EXACT "proof" was the cause of the promulgation of a NEW Axiom, in the field of mathematics. The reason for a NEW rule being created. Would ANY of you care to explain to me HOW 2 can equal 1? And WHAT the NEW rule was, that was created, as a consequence of this proof?
I'd appreciate reading what you have to say. And I'll give a Gold Star to the first one to explain this CORRECTLY, to me.