Intereting Posts

What are Diophantine equations REALLY?
Analytic solution of: ${u}''+\frac{1}{x}{u}'=-\delta e^{u}$
Unlike Jensen's Inequality, can we upper bound $\log \sum_{i}{u_i \exp(x_i)}$?
Is every monoid isomorphic to its opposite
uniqueness heat equation
Do finite algebraically closed fields exist?
Interpretation of Standard Deviation independent of the distribution?
Why is expectation defined by $\int xf(x)dx$?
Cauchy-Schwarz Inequality and Linear Dependence
Proving a relation between inradius ,circumradius and exradii in a triangle
Prove every strongly connected tournament has a cycle of length k for k = 3, 4, … n where n is the number of vertices.
Unexpected approximations which have led to important mathematical discoveries
Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$.
Show that if $A\subseteq B$, then inf $B\leq$ inf $A\leq$ sup $A \leq$ sup $B$
Studying mathematics efficiently

I know $R^\omega$ is the set of functions from $\omega$ to $R$. I would think $R^\infty$ as the limit of $R^n$, but isn’t that $R^\omega$?

The seem to be used differently, but I can’t tell exactly how.

- Does continuity depend on the distance function?
- Uniqueness of a continuous extension of a function into a Hausdorff space
- If $X$ is a connected metric space, then a locally constant function $f: X \to $ M, $M $ a metric space, is constant
- Real life applications of Topology
- How to show that disjoint closed sets have disjoint open supersets?
- Lebesgue measure as $\sup$ of measures of contained compact sets
- Characterizing continuous functions based on the graph of the function
- Construct a bijection between $\mathbb{Z}^+\times \mathbb{Z}^+$ and $\mathbb{Z}^+$
- Definition of metrizable topological space
- Connected metric spaces with at least 2 points are uncountable.

In a context where one makes a distiction between $R^\infty$ and $R^\omega$,

$R^\infty$ denotes the set of sequences with finite support whereas $R^\omega$ denotes the set of unrestricted sequences.

In this context, $R^\infty$ is the limit of $R^n$ when $n \to \infty$, in the sense that $R^\infty = \bigcup_{n=0}^{\infty} R^n$, with the convention that $R^n$ are all seen as subsets of $R^\omega$.

The two notations mean exactly the same thing. The second notation is more popular, as many mathematicians are not familiar with ordinal numbers.

- Dense subset of Cantor set homeomorphic to the Baire space
- The “Easiest” non-smoothable manifold
- A weak version of Markov-Kakutani fixed point theorem
- Multiple choice question: Let $f$ be an entire function such that $\lim_{|z|\rightarrow\infty}|f(z)|$ = $\infty$.
- Matrix theory textbook recommendation
- Show that a locally compact Hausdorff space is regular.
- $\Omega=x\;dy \wedge dz+y\;dz\wedge dx+z\;dx \wedge dy$ is never zero when restricted to $\mathbb{S^2}$
- Sequence satisfies weak law of large numbers but doesn't satisfy strong law of large numbers
- What is the value for $\lim_{x\to\infty} \frac{\sin x}{x}$?
- Brouwer's fixed point theorem implies Sperner's lemma
- Obstructions to lifting a map for the Hopf fibration
- Decidability of tiling of $\mathbb{R}^n$
- Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
- there exist two antipodal points on the equator that have the same temperature.
- Is there a function having a limit at every point while being nowhere continuous?