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I'm trying to prove the following exercise about the ortogonal symmetric group $so(n)$ It is clear that (in case he has a son) his son is born on some day of the week. I have been able to prove the first two sections of the exercise but i got.

Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$ A lot of answers/posts stated that the statement does matter) what i mean is The son lived exactly half as long as his father is i think unambiguous

Almost nothing is known about diophantus' life, and there is scholarly dispute about the approximate period in which he lived.

The simplest model assumes that there are 365 days in a year, each sibling having the same probability of 1/365 of being born on any of those days, and their births are independent That implies the probability that they have the same birthday is 1/365 You can make improvements on this model is various ways For example, you can include leap days

For that model you'd probably want to assume. If he has two sons born on tue and sun he will mention tue If he has a son & daughter both born on tue he will mention the son, etc. Are $so (n)\times z_2$ and $o (n)$ isomorphic as topological groups

I'm trying to show that so (n) is a compact topological group for every n

So (n) is the group of all nxn matrices m such that $m^ {t}m = i. What is the probability that their 4th child is a son (2 answers) closed 8 years ago As a child is boy or girl

This doesn't depend on it's elder siblings So the answer must be 1/2, but i found that the answer is 3/4 What's wrong with my reasoning Here in the question it is not stated that the couple has exactly 4 children

I am trying to figure out the formula for the quadratic casimir of the adjoint representation of so (n) but i can't find it anywhere

I know that for the spinorial. In case this is the correct solution Why does the probability change when the father specifies the birthday of a son

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