Skip to main content
MathOverflow

Return to Question

added 2 characters in body; edited title
Source Link
LeastSquare
LeastSquare
  • 93
  • 4

Is $ \{ \frac{1}{n} + \frac{1}{m} : n,m \in \mathbb{N} \}$ dense in anysome interval of $\mathbb{R}$?

Consider the set $\{\frac{1}{n} + \frac{1}{m}: n,m \in \mathbb{N} \}$. Is this set dense in anysome interval inof $\mathbb{R}$?

More generally let $S_k= \{\sum_{i=1}^k \frac{1}{n_i}: n_i \in \mathbb{N} \} $. Is this set dense in anysome interval inof $\mathbb{R}$?

I think the answer to both questions is no, but I was not able to come up with a proof. I am a physics student so I apologise if this question is naive for this website.

Is $ \{ \frac{1}{n} + \frac{1}{m} : n,m \in \mathbb{N} \}$ dense in any interval of $\mathbb{R}$?

Consider the set $\{\frac{1}{n} + \frac{1}{m}: n,m \in \mathbb{N} \}$. Is this set dense in any interval in $\mathbb{R}$?

More generally let $S_k= \{\sum_{i=1}^k \frac{1}{n_i}: n_i \in \mathbb{N} \} $. Is this set dense in any interval in $\mathbb{R}$?

I think the answer to both questions is no, but I was not able to come up with a proof. I am a physics student so I apologise if this question is naive for this website.

Is $ \{ \frac{1}{n} + \frac{1}{m} : n,m \in \mathbb{N} \}$ dense in some interval of $\mathbb{R}$?

Consider the set $\{\frac{1}{n} + \frac{1}{m}: n,m \in \mathbb{N} \}$. Is this set dense in some interval of $\mathbb{R}$?

More generally let $S_k= \{\sum_{i=1}^k \frac{1}{n_i}: n_i \in \mathbb{N} \} $. Is this set dense in some interval of $\mathbb{R}$?

I think the answer to both questions is no, but I was not able to come up with a proof. I am a physics student so I apologise if this question is naive for this website.

Post Closed as "Not suitable for this site" by Mateusz Kwaśnicki, Todd Trimble
Source Link
LeastSquare
LeastSquare
  • 93
  • 4

Is $ \{ \frac{1}{n} + \frac{1}{m} : n,m \in \mathbb{N} \}$ dense in any interval of $\mathbb{R}$?

Consider the set $\{\frac{1}{n} + \frac{1}{m}: n,m \in \mathbb{N} \}$. Is this set dense in any interval in $\mathbb{R}$?

More generally let $S_k= \{\sum_{i=1}^k \frac{1}{n_i}: n_i \in \mathbb{N} \} $. Is this set dense in any interval in $\mathbb{R}$?

I think the answer to both questions is no, but I was not able to come up with a proof. I am a physics student so I apologise if this question is naive for this website.