11
votes
7answers
1k views

What's wrong with these equations? [duplicate]

My friend Boris (Boryan) gave me a task, and completely refuses to give the answer what's wrong here. $$x^2=\overbrace{x+\cdots+x} ^{x\text{ times}}$$ $$(x^2)'=(x+\cdots+x)'$$ $$2x=1+\cdots+1$$ ...
0
votes
3answers
74 views

In sphere $r \propto \frac{1}{A}$! How is this possible? What's the wrong here?

Surface area $A$ and volume $V$ of a sphere of radius $r$ are \begin{eqnarray} A=4\pi r^2,\\ V=\frac{4}{3} \pi r^3. \end{eqnarray} But then \begin{align} \frac{V}{A} & = \frac{r}{3}\\ ...
-1
votes
1answer
87 views

Two equal to One? Is it correct?

Some people ask me that two, Two equal to One ...
3
votes
3answers
671 views

What is wrong with this proof of: $2+2 = 5$ [duplicate]

I have seen this image and surprised that we can prove $2 + 2 = 5$. can any one tell me what is wrong with this image. Prove that, $2+2=5$. We know that, $2+2=4$ ...
2
votes
2answers
299 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 = ...
13
votes
12answers
3k 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
119 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
110 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
192 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 ...