All Questions
3
questions
3
votes
1
answer
433
views
Why is $\mathbb{R}/\mathbb{Z}$ not an $\mathbb{R}$-vector space?
This is an embarrassing question which might seem elementary and possibly silly, but its suddenly confusing me. Clearly I'm missing something very obvious.
Take the structure $\mathbb{R}/\mathbb{Z}$. ...
- 2,517
1
vote
1
answer
85
views
Are these two mathematical objects the same from a practical standpoint, or literally identical mathematical objects? [closed]
This question is derived from another question that I recently asked.
Take the two mathematical objects $\{ \mathbf{x} \in \mathbb{R}^n \mid x_1, x_2, \ldots, x_n \in \mathbb{Z} \}$ and $\{ \mathbf{x}...
- 4,312
4
votes
1
answer
710
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$n$-dimensional integer space? Or $\{ \mathbf{x} \in \mathbb{R}^n | x_1, x_2, ..., x_n \in \mathbb{Z} \}$?
If $\mathbf{x} \in \mathbb{R}^n$, then we would have $x_1, x_2, ..., x_n \in \mathbb{R}$, right? This is commonly known as $n$-dimensional space.
My question is, could we also have such a thing as $\...
- 4,312