Question

I have a question about vector fields - I'll write it in comment

Answer 1

is set \[S=\left\{ \left( x _{1}, ..., x _{n} \right)\in \mathbb{R} ^{n} | x _{i}\in \mathbb{Z} \forall i \right\}\] subspace of \[\mathbb{R} ^{n}\]?
That is problem. My question is : from which field scalars are?
From \[\mathbb{R}\]?

Answer 2

To be a subspace a zero element must exist, but as x is an integer this is met.
x_i+x_j = x_k is also an integer, so this condition is met.
But for some scalar c, namely c not an integer, cx_i is NOT an integer. This means that S is not a subspace of R^n.

Answer 3

And I assume scalars are from R.

Answer 4

thanks :)