Injection from R2 to R
Find an injection from $\mathbb R^2\to\mathbb R$.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: Injection from R2 to R
Interesting. A classic space-filling curve should work. Are there easier solutions?
Re: Injection from R2 to R
Should be, as it was on one of our examples sheets. And I don't even know what that term means
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: Injection from R2 to R
There's one that maps all the points in $(0,1) \times (0,1)$ to $(0,1)$. Take $(0.a_1a_2a_3 ... ,0.b_1b_2b_3 ...) \rightarrow 0.a_1b_1a_2b_2a_3b_3...$. Such a map should work also
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor
Re: Injection from R2 to R
Yep that should work.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein