# Tag Info

### Rigrous proof of the rate and order of convergence of bisection method

No, you can not apply this Q-convergence rate formula, in many cases the sequence of quotients has no limit. It is only the interval length, which is an upper error bound, that converges that way to ...
• 128k
1 vote

• 574

### Nonstandard Analysis research project ideas

There are two approaches to non-standard analysis: (1) the "extension" approach and (2) the axiomatic approach. In the "extension" approach, the real numbers are extended to the ...
• 43.8k
Accepted

### Translates of a set of positive Lebesgue measure cover $\mathbb{R}$?

Let $E$ be fat Cantor set (i.e. a Cantor like set of positive measure). Then $E$ has no interior. If $\mathbb R=\bigcup_n (E+x_n)$ then Baire Category Theorem implies that $E+x_n$ has an intetior ...
• 39.3k
Accepted

### How to show that the limit of a sequence is not equal to some value?

I will clarify my comment. By definition, $l$ is the limit of the sequence $a_n$ if for every $\varepsilon>0$ you can find $N$ such that $\left|a_n-l\right|<\varepsilon$ for all $n>N$. Thus, ...
• 139
1 vote
Accepted

• 17k