All Questions
3
questions
4
votes
3
answers
4k
views
Is the Cantor Pairing function guaranteed to generate a unique real number for all real numbers?
I recently learned that for natural numbers, the Cantor Pairing function allows one to output a unique natural number from any combination of two natural numbers. According to wikipedia, it is a ...
- 43
0
votes
0
answers
60
views
Find the closest/next $x\in\mathbb{N}$ that satisfies the equation $Ⲭ_{\mathbb{N}}(f(x)) = 1$.
Find the closest/next $x\in\mathbb{N}$ that satisfies the equation $Ⲭ_ℕ(f(x)) = 1$, where $Ⲭ_\mathbb{N}(x): \mathbb{R} \rightarrow \mathbb{N}$ is defined by
$$
\begin{cases}
1 &\text{if } f(x) \...
- 1
1
vote
1
answer
34
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How to prove $2^{\sqrt{f(n)}} \in O\ (2^{f(n)})$ if $f:\Bbb{N}\rightarrow \Bbb{R^+}$?
How to prove $2^{\sqrt{f(n)}} \in O\ (2^{f(n)})$ if $f:\Bbb{N}\rightarrow \Bbb{R^+}$?
So we want to prove $\exists c\in\Bbb{R^+}:\ [\exists B\in\Bbb{N}:[\ \forall
n\in\Bbb{N}:\ n\ge B\rightarrow 2^{\...
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