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## “Thankfully” in Spanish?

Would it be correct to say, Hoy es llueve, salvos afortunadamente, manana es hace sol. when trying to say Today is rainy, but thankfully tomorrow is sunny. If not, what would I say ...

3 answers | 39 secs ago by user1 on spanish.stackexchange.com

## When are cancellations allowed in ring?

During the lecture my professored mentioned something like "cancellation is perfectly fine in a ring when dealing with addition, but not with multiplication!". The example he gave was that, in ...

## Using Math.SE as a contest site

This isn't the usual issue about questions from contest competitions being posted here for assistance, but rather about the use of Math.SE as a venue for hosting a "contest" using a future bounty as ...

5 answers | 52 secs ago by hardmath on meta.math.stackexchange.com

## >Prove that for any nonzero vectors $\bf u$ and $\bf a$ in $\Bbb R^n$, the vector $\bf a$ is orthogonal to ${\bf u} - \mathrm{proj}_{\bf a}{\bf u}$.

Prove that for any nonzero vectors $\bf u$ and $\bf a$ in $\Bbb R^n$, the vector $\bf a$ is orthogonal to ${\bf u} - \mathrm{proj}_{\bf a}{\bf u}$. I'm not sure how to start proving this. I don't ...