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1=2: A Proof using Beginning Algebra. The Fallacious Proof: Step 1: Let a = b . Step 2: Then , Step 3: , Step 4: , Step 5: , Step 6: and . Step 7: This can be written as , Step 8: and cancelling the from both sides gives 1=2. See if you can figure out in which step the fallacy lies.
- Step 7
This step is not the source of the fallacy. This follows...
- This is Not The Fallacy
This step is not the source of the fallacy. The phrase "let...
- Classic Fallacies
Classic Fallacies Our mathematical correspondent has just...
- Text-Only Version
Step 8: and cancelling the (a^2 - ab) from both sides gives...
- A Proof Using Complex Numbers
Complex Numbers This proof uses complex numbers. For those...
- Step 7
12 Ιουλ 2022 · Some people think that 1=2, and the math actually makes sense. But can you prove them wrong and find the flaw in their logic?
Prove that there are no natural numbers \(a\) and \(n\) with \(n \ge 2\) and \(a^2 + 1 = 2^n\). Are the following propositions true or false? Justify each conclusions with a counterexample or a proof.
17 Ιουν 2014 · To show is to use numbers to demonstrate a certain property, to prove it to use letters to prove that the system works for all number systems. There is a clear difference that can really hurt you in exam questions and assignments.
13 Ιουν 2020 · By the distributive law, $(x + 1)(x - 1) = x^2 - 1$. Set $x = -1$ and observe that the left hand side is zero, so the right hand side is zero, so $x^2 = 1$. It's arguable whether the assumptions I use there are any more or less obvious than the conclusion.
25 Ιουλ 2011 · To prove 1+1=2, you have to define what is 1,+,= and 2. They are all simple literals that can mean anything. Without definition, 2 doesn't have to be the number of eyes a person has.
15 Ιαν 2013 · The work of G. Peano shows that it's not hard to produce a useful set of axioms that can prove 1+1=2 much more easily than Whitehead and Russell do. The later theorem alluded to, that $1+1=2$, appears in section $\ast110$:
