# All Questions

168 views

### When is this set a field?

For which $c$ will the set $K(c) = \{a + b\sqrt{c} : a, b \in \mathbb{Q}\}$ be a field? I know for example, that $K(\frac{2}{3})$ will be one, I am just wondering what the most general result of this ...
330 views

1k views

### Understanding direct sum of matrices

I read the definition of direct sum on wikipedia, and got the idea that a direct sum of two matrices is a block diagonal matrix. However this does not help me understand this statement in a book. In ...
360 views

### How to prove that proj(proj(b onto a) onto a) = proj(b onto a)?

How to prove that proj(proj(b onto a) onto a) = proj(b onto a)? It makes perfect sense conceptually, but I keep going in circles when I try to prove it mathematically. Any help would be appreciated.
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### One-reducibility extending to onto function

I'm working on the following problem from Soare: If $A$ is one-reducible to $B$ ($A \leq_1 B$) and $A, B$ c.e., $A$ infinite then $A$ is one-reducible to $B$ via some $f$ such that $f(A)=B$. I know ...
419 views

### Asymptotics of LCM

Let $\operatorname{LCM}(x_1,x_2,\ldots,x_n)$ be the least common multiple of the integers $x_i$. How can one find the asymptotics of $\operatorname{LCM}(f(1),f(2),\dots,f(n))$ as $n$ approaches ...
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99 views

### How can I calculate $\sum\limits_{i=1}^n\cfrac{n}{2^n}$ [duplicate]

Possible Duplicate: How to find the sum of this infinite series How can I calculate result of $\sum\limits_{i=1}^n\cfrac{n}{2^n}$ ?