Injection from R2 to R

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nayel
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Injection from R2 to R

Unread post by nayel » Sun Mar 06, 2011 4:24 pm

Find an injection from $\mathbb R^2\to\mathbb R$.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein

tanvirab
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Re: Injection from R2 to R

Unread post by tanvirab » Mon Mar 07, 2011 2:51 am

Interesting. A classic space-filling curve should work. Are there easier solutions?

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nayel
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Re: Injection from R2 to R

Unread post by nayel » Mon Mar 07, 2011 4:16 pm

Should be, as it was on one of our examples sheets. And I don't even know what that term means :P
"Everything should be made as simple as possible, but not simpler." - Albert Einstein

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Avik Roy
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Re: Injection from R2 to R

Unread post by Avik Roy » Wed Mar 23, 2011 12:27 am

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
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nayel
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Re: Injection from R2 to R

Unread post by nayel » Thu Mar 24, 2011 5:56 pm

Yep that should work.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein

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