Intereting Posts

Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$
How many numbers between $1$ and $9999$ have sum of their digits equal to $8$? $16$?
Deducing a $\cos (kx)$ summation from the $e^{ikx}$ summation
Equicontinuity and uniform convergence 2
Why is F a UFD?
Integral $\int\!\sqrt{\cot x}\,dx $
Separable First Order Ordinary Differential Equation with Natural Logarithms
Integral of $1/z$ over the unit circle
Construction of special $\omega_1$-Aronszajn tree
Minimal number of moves to construct the challenges (circle packings and regular polygons) in Ancient Greek Geometry?
Homology and Graph Theory
Arrange the following growth rates in increasing order: $O (n (\log n)^2), O (35^n), O(35n^2 + 11), O(1), O(n \log n)$
Categories with limits for large diagrams
Combinatorial interpretation of a sum identity: $\sum_{k=1}^n(k-1)(n-k)=\binom{n}{3}$
How to find $E(X|X+Y=k)$ for geometrical distribution?

Is the cardinality of

$$X = \{f: \Bbb R \to \Bbb R \;|\; f \text{ is differentiable everywhere}\}$$

the same as $\Bbb R$?

How to prove it?

- How to divide aleph numbers
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- $\infty$ and $-\infty$ are to $\aleph_0$ / $\beth_0$ as “what” is to $\beth_1$?
- Does it make sense to define $ \aleph_{\infty}=\lim\limits_{n\to\infty}\aleph_n $? Is its cardinality “infinitely infinite”?
- Do you need the Axiom of Choice to accept Cantor's Diagonal Proof?

Hint: This is also true of the set of *continuous* functions from $\mathbb{R}$ to $\mathbb{R}$, which contains all differentiable functions. Try using the fact that a continuous function is determined by its values on the rational numbers (a countable set).

- Showing $x^{5}-ax-1\in\mathbb{Z}$ is irreducible
- Prove that $2^{n(n+1)}>(n+1)^{n+1}\left(\frac{n}{1}\right)^n\left(\frac{n-1}{2}\right)^{n-1}\cdots \left(\frac{2}{n-1}\right)^{2}\frac{1}{n}$
- $\int\limits_{0}^{\pi/2}\frac{1+2\cos x}{(2+\cos x)^2}dx$
- Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$?
- The maximal subfield of $\mathbb C$ not containing $\sqrt2$
- Prob. 26, Chap. 5 in Baby Rudin: If $\left| f^\prime(x) \right| \leq A \left| f(x) \right|$ on $$, then $f = 0$
- Not Skolem's Paradox – Part 3
- When does the topological boundary of an embedded manifold equal its manifold boundary?
- What are the prerequisites to Jech's Set theory text?
- What does it mean to show that something is well defined?
- What is the best way to factor arbitrary polynomials?
- Does taking the direct limit of chain complexes commute with taking homology?
- Prove that if $f$ is bounded and nondecreasing on $(a,b)$ then lim $f(x) $as $x$ approaches $b$ from the left exists.
- How do I substitute a value into a polynomial in GAP?
- Orthonormal vectors in Polar coordinates, show $\hat{e}_R=\frac{(x,y,z)}{r}$