518 Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real? 125 What is lost when we move from reals to complex numbers? 68 Abusing mathematical notation, are these examples of abuse? 62 Mathematical ideas that took long to define rigorously 60 Why does Wolfram Alpha say that $\infty^\infty$ results in “complex infinity”?

### Reputation (33,099)

 +10 Why does Wolfram Alpha say that $\infty^\infty$ results in “complex infinity”? -2 Abusing mathematical notation, are these examples of abuse? +10 Do Gödel numbers have a practical use? +10 Why is this inequality true? $(a+b)^2\leq 2(a^2+b^2)$

### Questions (15)

 3 Poset is complete iff it is cocomplete 3 Discrete posets are projective 3 $\mathbf{Set} \not \simeq \mathbf{Set}^*$ by considering $\{1, 2 \} \to \{1\}$ 2 Injective objects in the category of posets 2 Limit of a certain sum

### Tags (336)

 662 complex-numbers × 9 214 real-analysis × 88 526 recursion × 10 186 logic × 66 518 continued-fractions 184 elementary-set-theory × 84 314 abstract-algebra × 49 154 limits × 55 246 definition × 21 150 functions × 42

### Bookmarks (17)

 98 A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent 46 Find the limit $L=\lim_{n\to \infty} \sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt[n]{\frac{1}{n}}}}$ 25 Sudoku with special properties 20 Find all functions $f: \mathbb N \rightarrow \mathbb N$ such that $f(n!)=f(n)!$ 18 Power series which diverges precisely at the roots of unity, converges elsewhere