For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
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discrete mathematics - Show $|u^n| = n|u|$ for all strings $u$ and …
Can anyone please help me with this homework question on automata from Peter Linz? Use induction on $n$ to show that $|u^n| = n|u|$ for all strings $u$ and all $n$.
modular arithmetic - Prove that that $U (n)$ is an abelian group ...
Prove that that $U(n)$, which is the set of all numbers relatively prime to $n$ that are greater than or equal to one or less than or equal to $n-1$ is an Abelian ...
Prove that the order of $U (n)$ is even when $n>2$.
Right! I like that: $ (n-1)^2=n^2-2n+1=n (n-2)+1 \equiv 1 (\bmod {n})$. I was skeptical of the line "However, we know (I forgot the theorem's name) that the number of elements of order 2 is …
Suppose that $ (x_n)$ and $ (y_n)$ are convergent sequences and …
Suppose that $ (x_n)$ and $ (y_n)$ are convergent sequences and let un=min {xn,yn}. Prove that (un) is a convergent sequence Ask Question Asked 11 years, 1 month ago Modified 11 years, …
Prove that the sequence (1+1/n)^n is convergent [duplicate]
Mar 27, 2019 · I know the proof using binomial expansion and then by monotone convergence theorem. But i want to collect some other proofs without using the binomial expansion. *if you …
How do we calculate factorials for numbers with decimal places?
I was playing with my calculator when I tried $1.5!$. It came out to be $1.32934038817$. Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\\times1$, but how do …
Proof that $U (n)$ is connected - Mathematics Stack Exchange
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When is the group of units in $\\mathbb{Z}_n$ cyclic?
Let $U_n$ denote the group of units in $\\mathbb{Z}_n$ with multiplication modulo $n$. It is easy to show that this is a group. My question is how to characterize the ...
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