The video presents a seemingly valid algebraic proof that 1 equals 2. It begins by setting two variables, 'a' and 'b', equal to each other (a = b). The proof then proceeds by multiplying both sides by 'a', resulting in a^2 = ab. Next, it subtracts b^2 from both sides, leading to a^2 - b^2 = ab - b^2. The left side is then factored as a difference of squares (a - b)(a + b), and the right side has a greatest common factor of 'b' factored out, resulting in b(a - b). At this point, the proof cancels the term (a - b) from both sides, leaving a + b = b. Since the initial assumption was a = b, 'a' is substituted with 'b' in the equation, yielding b + b = b, which simplifies to 2b = b. Finally, dividing both sides by 'b' leads to the conclusion that 2 = 1. The video then reveals the flaw in the proof: the initial assumption that a = b means that (a - b) is equal to zero. Dividing by zero is an undefined operation in algebra, and therefore, canceling (a - b) from both sides is an invalid step that invalidates the entire proof.

BriTheMathGuy

What a great way to show that one equals two! Just let a equal B and multiply both sides by a. Next, subtract B squared from both sides so we can factor both sides. On the left, we have a difference of squares, and on the right, we have a greatest common factor of B. We'll just pull that out. Now, just using standard algebraic rules, cancel a minus B on both sides. We have a plus B equals B. But we assumed that a was B to begin with, so a plus B means the same as B plus B. So, 2B equals B, and dividing both sides by B gives us two equals one.

What went wrong algebraically? Since we assumed a equals B, then the quantity a minus B has to be zero, and we're not allowed to cancel zero on both sides. We can't divide by zero.

1=2 Proof

what a great way to show that one equals
two just let a equal B and multiply both
sides by a next subtract B squared from
both sides so we can Factor both sides
on the left we have a difference of
squares and on the right we have a
greatest common factor of B we'll just
pull that out now just using standard
algebraic rules cancel a minus B on both
sides we have a plus b equals B but we
assumed that a was B to begin with
so a plus b means the same as B plus b
so 2B equals B and dividing both sides
by B gives us two equals one what went
wrong algebraically since we assumed a
equals B then the quantity a minus B has
to be zero and we're not allowed to
cancel zero on both sides we can't
divide by zero

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1=2 Proof

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