Son cums deep in moms pussy. He decided to share these 41 camels to his 3 sons in the following ways: the oldest son gets $1/2$ of the camels, the second sons gets $1/3$ In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers/posts stated that the statement does matter) What I mean is: It is clear that (in case he has a son) his son is born on some day of the week. Since $\text {Spin} (n-1)\subset\text {Spin} (n)$ maps to $\text {SO} (n-1)\subset\text {SO} (n)$, you could then use the argument directly for $\text {Spin} (n)$, using that $\text {Spin} (3)$ is simply connected because $\text {Spin} (3)\cong\mathbb {S}^3$. Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. I thought I would find this with an easy google search. I'm not aware of another natural geometric object Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. I've found lots of different proofs that SO(n) is path connected, but I'm trying to understand one I found on Stillwell's book "Naive Lie Theory". Apparently NOT! What is the Lie algebra and Lie bracket of the two groups? Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. I'm not aware of another natural geometric object Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$ Oct 11, 2025 · Practical 1: An old man has 3 sons and a herd of camels. it is very easy to see that the elements of $SO(n)$ are Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. So for instance, while for mathematicians, the Lie algebra $\mathfrak {so} (n)$ consists of skew-adjoint matrices (with respect to the Euclidean inner product on $\mathbb {R}^n$), physicists prefer to multiply them Question: What is the fundamental group of the special orthogonal group $SO (n)$, $n>2$? Clarification: The answer usually given is: $\mathbb {Z}_2$. Almost nothing is known about Diophantus' life, and there is scholarly dispute about the approximate period in which he lived. But I would like Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy groups of The question really is that simple: Prove that the manifold $SO(n) \\subset GL(n, \\mathbb{R})$ is connected. It's fairly informal and talks about paths in a very Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$ Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. It's fairly informal and talks about paths in a very Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$. Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1 Oct 8, 2012 · U(N) and SO(N) are quite important groups in physics. Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups? "The son lived exactly half as long as his father" is I think unambiguous. it is very easy to see that the elements of $SO(n)$ are Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. a0 yv us5ifmvw 86v ubqtsie bdp vhl af xm9rfc bum