query: How to show $2^{ℵ_0} \leq \mathfrak c$
positive_passages.docid: 20281
positive_passages.text: Easiest way to prove that $2^{\aleph_0} = c$
negative_passages.docid: 14951
negative_passages.text: Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$
negative_passages.docid: 104498
negative_passages.text: Show that $x^3y^3(x^3+y^3) \leq 2$
negative_passages.docid: 47323
negative_passages.text: Show that $\left(1+\frac xk\right)^k$ is monotonically increasing
negative_passages.docid: 57670
negative_passages.text: Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
negative_passages.docid: 105641
negative_passages.text: Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
negative_passages.docid: 39270
negative_passages.text: Showing that $e^x > 1+x$
negative_passages.docid: 13902
negative_passages.text: Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
negative_passages.docid: 5043
negative_passages.text: Show that $2^n>1+n\sqrt{2^{n-1}}$
negative_passages.docid: 91877
negative_passages.text: Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 116387
negative_passages.text: How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
negative_passages.docid: 52642
negative_passages.text: Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
negative_passages.docid: 106609
negative_passages.text: Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
negative_passages.docid: 45205
negative_passages.text: Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
negative_passages.docid: 21921
negative_passages.text: Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
negative_passages.docid: 52353
negative_passages.text: Bounding Euler's e by showing $2 \leq \left (1+ \frac{1}{n}\right)^n < 3$