![False Proof of 1=-1 [duplicate]](https://news.conceivablytech.com/uploads/false-proof-of-1-1-duplicate_720.jpg)
general
False Proof of 1=-1 [duplicate]
I found the following proof online and am confused as to where the error occurs. $1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}=(\sqrt{-1})^2=-1$ My guess...
Apr 16, 2026
Archive: General
general
What is the agreed upon definition of a "positive definite matrix"?
In here: http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/positive-definite-matrices-and-applications/symmetric-matrices-and-positi...
Apr 16, 2026
general
Difference : subsequences and substrings
What are the differences between subsequences and substrings?
Apr 16, 2026
general
Implementing Bates distribution
I've been trying to plot the Bates distribution curve, The Bates distribution is the distribution of the mean of n independent standard uniform varia...
Apr 16, 2026
general
Find the value of $\sin (x)$ if $\cos(x)=\frac 1 3$
$$\cos (x)=\left (\frac{1}{3}\right)$$for $0°\lt\ x\lt90°$ Find the exact value of $\sin(x)$. Give your answer as a surd. I found the value with my calcul...
Apr 16, 2026
general
Implicit differentiation $x = e^{xy}$
I have a question regarding the problem below... Using implicit differentiation, what is the derivative of $x = e^{x y}$? I believe this is using a chain ...
Apr 16, 2026
general
Existence of the Pfaffian?
Consider a square skew-symmetric $n\times n$ matrix $A$. We know that $\det(A)=\det(A^T)=(-1)^n\det(A)$, so if $n$ is odd, the determinant vanishes. If $n...
Apr 16, 2026
general
Vakil's FOAG, Exercise 9.2.K: Transcendental Complex Numbers
How does one realize a transcendental complex number as a maximal ideal of $\mathbb{Q}(t) \otimes_{\mathbb{Q}} \mathbb{C}$? This is the essence of Exercis...
Apr 16, 2026
general
Why are weak topologies useful in functional analysis?
I've been reading through chapter 3, Rudin's Functional Analysis, and an important point is the one of weak topology. From the theorems it seems...
Apr 16, 2026
general
Product of a and b should be equal to the sum of all numbers in the sequence excluding a and b
I came across the below question in codewars. Regarding to the question, all I know is the sum of numbers ranging from 1 to n is $n(n+1)/2$. And I have no...
Apr 16, 2026
