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Suppose I want to prove $a=b$.

I start by assuming $a=b$. I simplify the expressions and arrive at something which is always true like $1=1$. Does this mean that the original statement is true?

Ryder Rude
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    I want to prove $1 = 2$. I start by assuming $1 = 2$. I multiply both sides by $0$ to simplify it and arrive at $0 = 0$, which is true. Is the original statement true? –  Feb 06 '18 at 02:57
  • @user296602 I get it. Thanks. – Ryder Rude Feb 06 '18 at 02:57
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    You're welcome. It's good that you asked - I see far too many students just assume that it's a valid technique, and do it over and over again..... –  Feb 06 '18 at 03:01
  • I see this mistake all too often in inductive proofs... – Bram28 Feb 06 '18 at 03:10

3 Answers3

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This is called circular reasoning and it's not sound because you're assuming the conclusion to begin with.

Akababa
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$-1=1 \implies (-1)^2=1^2 \implies 1=1$.

But $-1=1$ is obviously not true.

CY Aries
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Are you referring to Deduction? Typically this is not done, you usually do it in reverse, arriving at the statement you want to prove from something you know to be true like $1=1$ by reasoning deductively and manipulating both sides of the equation.

Harry Alli
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