Questions tagged [fake-proofs]
Seemingly flawless arguments are often presented to prove obvious fallacies (such as 0=1). This is the appropriate tag to use when asking "Where is the proof wrong?" about proofs of such obvious fallacies.
830
questions
0
votes
1answer
24 views
Geodesic flow in $T^\ast M$ is the Hamiltonian
Let $(M, g)$ be a smooth Riemannian manifold and let $\gamma : [0,1] \to M$ be a geodesic. Then in local co-ordinate $(x_1, \dots, x_n)$ where $x_i(t) = \gamma_i(t)$ and we set $v_i(t) = \dot{x}_i(t)$...
3
votes
4answers
51 views
Can anyone help me what's wrong here as i can prove 0 = 1?
Suppose
S = 1 + 1 + 1 + 1 ....
and hence we can write
S = 1 + S
therefore,
1 = 0
This seems absurd to me but where am I going wrong here? or is it some paradox
10
votes
4answers
2k views
Can't understand an ACT practice problem: Triangle appears to be isosceles, why isn't the answer $7.3\sim $ here?
In the following picture, $XY = YZ$, $\angle a = 40^\circ$, and the length opposite is $5$.
The problem asks to compute $XY$
We immediately dropped the dotted perpendicular and get two right ...
11
votes
5answers
1k views
Why doesn't this proof show that the operation on a factor group is well-defined?
Suppose $G$ is a group and let $H \triangleleft G$. Consider the factor group $G/H$ where the relation is $aHbH = abH$ for all $a,b \in G$.
Suppose we wanted to show that the above relation is well-...
6
votes
2answers
130 views
Prove a result by assuming it's true and showing no contradiction
Preface: I'm not too experienced in propositional logic, just the basics, and I'm familiar with common proof methods (modus ponens, modus tollens, reductio ad absurdum, etc) but not so familiar to be ...
19
votes
1answer
785 views
Proof that every field is perfect?
The following must be wrong, since it shows that every field is perfect, which I gather is not so. But I can't find the error:
Suppose $E/K$ is a field extension and $p\in K[x]$ is irreducible ...
9
votes
5answers
321 views
Where is the mistake in my 'derivation' of $(uv)' = u'v$?
So I tried to derive the product rule without adding $f(x)g(x+\Delta x)-f(x)g(x+\Delta x)$ as we used to. Instead I started deriving it directly and ran into a strange conclusion that $(uv)'=u'v$. The ...
1
vote
1answer
34 views
Wrong intuition about counting number of surjections
Consider the sets $A:= \{1, 2, 3, 4\}$ and $B:= \{1,2,3\}$. It is not hard to count the number of surjections $A \to B$, namely $36$, by subtracting the number of non-surjections from $81$.
But I'm ...
0
votes
0answers
42 views
Fake proof: there are no highest weights for representations of $\mathfrak{sl}(2)$
Let $\pi$ be a representation a $\mathfrak{sl}(2)$. Let $v$ be a highest weight vector, with $\Lambda$ the highest weight.
Then we must have $\pi(H)\pi(E^+)v=0$. But $\pi(H)$ has zero kernel, meaning ...
8
votes
3answers
2k views
What is the problem here (all integers are irrational proof…I think so)?
Let us assume $a$ is an integer which is rational which implies $a=p/q$ (where $p$ and $q$ are integers and $q$ not equal to $0$). If $p$ and $q$ are not coprime, let us simplify the fraction so this ...
1
vote
0answers
16 views
Contradiction in Conditions for Theorem for comparison of Markov Chains?
In this paper ( here: https://epubs.siam.org/doi/pdf/10.1137/1122004 or here: https://www.tandfonline.com/doi/pdf/10.1080/02331887608801286?needAccess=true) by Kirstein, Franken and Stoyan, the ...
1
vote
2answers
102 views
Confusion about Trapezoid rule error
The error of the trapezoid rule is often derived using the Mean Value Theorem, which is used to get that $\frac{f'(b)-f'(a)}{b-a}=f''(c)$ for some $c\in[a,b]$. The actual error is $-\frac{(b-a)^3}{12N^...
6
votes
1answer
68 views
Let $G$ be a $p$-group: $|G| = p^r$. Prove that $G$ contains a normal subgroup of order $p^k$ for every nonnegative $k \le r$.
Let $p$ be a prime number, and let $G$ be a $p$-group: $|G| = p^r$. Prove that $G$ contains a normal subgroup of order $p^k$ for every nonnegative $k \le r$.
The answers here and here use induction ...
4
votes
3answers
58 views
What is wrong with this induction proof? I am confused on how this is wrong other than the base case being wrong.
P(n): $n=2n$ for all integers $n >= 0$
Base Case: n = 0
Verify Base Case:
P(0): 0 = 2(0) which is true
Induction Step:
Assume that P(n) is true. Then multiply both sides of the quantity by $(n+...
7
votes
1answer
104 views
A “proof” for $0=1$ by integrating $\int \frac{dx}{x\ln x}$ by parts [duplicate]
Let's consider the indefinite integral $$\int \frac{dx}{x\ln x}.$$
We will compute it by integrating by parts:
$$\int \frac{dx}{x\ln x}=\int (\ln x)'\frac{dx}{\ln x}=1+\int \frac{dx}{x\ln x}.$$
Hence, ...
