# Tagged Questions

2answers
88 views

### Flawed proof that all positive integers are equal

Suppose that we are trying to prove that for every positive integer n, if x and y are positive integers with max(x, y) = n, then x = y. For the base case, we suppose n = 1. If max(x, y) = 1 and x and ...
8answers
2k views

### There are no bearded men in the world - What goes wrong in this proof?

Several years ago in a textbook I read this example as a faulty use of proof by induction. I never really realized why it fails. Here it goes: Theorem. There are no bearded men in the world. ...
12answers
3k views

### All natural numbers are equal.

I saw the following "theorem" and its "proof". I can't explain well why the argument is wrong. Could you give me clear explanation so that kids can understand. Theorem: All natural numbers are ...
2answers
107 views

### Find the demonstration error for the statement “All positive integers are equal”

All positive integers are equal, that is, for each $n \in \mathbb{N}$ the assertion $P(N): 1 = \cdots = n$ is true. (i) $P(1)$ is true because $1 = 1$ (ii) Suppose that $P(n)$ is true, then \$1 = ...
1answer
89 views

### Find the fallacy in the following treatment

Claim: any two positive integers are equal Proof: Let $A(n)$ be statement: if $a$ and $b$ are any two positive integers such that $\max(a,b)=n$ then $a=b$ Suppose $A(r)$ is true. Let ...
1answer
202 views

### Explain what’s bogus about the proof.

I couldn't find what is wrong with this strong induction proof, any one knows ? Question: A sequence of numbers is weakly decreasing when each number in the sequence is $\geq$ the numbers after it. ...
3answers
516 views

### Fake induction proof

Using the induction method: $(\forall P)[[P(0) \land ( \forall k \in \mathbb{N}) (P(k) \Rightarrow P(k+1))] \Rightarrow ( \forall n \in \mathbb{N} ) [ P(n) ]]$ Why this proof is wrong? \$P(x)\equiv ...
2answers
2k views

### Proof of 1=0 by mathematical induction?

I got stuck with a problem that pop up in my mind while learning limits. I am still a high school student. $\lim\limits_{n\to\infty}(\underbrace{\frac{1}{n}+\frac{1}{n}+\cdots+\frac{1}{n}}_{m})=0$ ...
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