Tagged Questions
2
votes
2answers
108 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 = ...
11
votes
12answers
2k views
Funny thing. Multiplying both the sides by 0?
Alright this maybe really funny but I want to know why is this wrong. We often come across identities which we prove by multiplying both the sides of the identity by a certain entity but why don't we ...
4
votes
3answers
101 views
Through any $n$ distinct points on a plane we can draw a straight line.
I can't understand what is wrong with this paradox. How we should strictly mathematically explain it?
Mathematical induction:
1. The basis:
$n=1,n=2$. Through any two (one) points on a plane we ...
3
votes
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 ...
5
votes
2answers
129 views
Fake proof of the limit of a series
Now, I know this to be correct:
$$\begin{align*}
\lim_{n \rightarrow\infty} \left(\frac 1{n^2}+\frac 2{n^2}+\ldots+\frac n{n^2}\right)&=\lim_{n \rightarrow\infty} \left[\frac 1{n^2} \left(\frac ...
