Intereting Posts

How can I prove that $\int_{0}^{\infty }\frac{\log(1+x)}{x(1+x)}dx=\sum_{n=1}^{\infty }\frac{1}{n^2}$
Algebra: What allows us to do the same thing to both sides of an equation?
Contradicting Fubini's theorem
Integrals involving reciprocal square root of a quartic
Combinatorial Proof Question
Locally connected and compact Hausdorff space invariant of continuous mappings
Equivalence for Christoffel symbol and Koszul formula
Prove that $\sum\limits_{A\subseteq }\sum\limits_{B\subseteq } |A\cap B|=n4^{n-1}$
Proving a polynomial $f(x)$ composite for infinitely many $x$
Show that the cube of any integer is congruent to $0$ or $\pm 1 \pmod 7 $
Solving recurrence relation in 2 variables
What is the function for a 'fractal sine wave'?
Is total boundedness a topological property?
Are there infinitely many primes next to smooth numbers?
Can someone explain consensus theorem for boolean algebra

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.

- What is the relation between the usual topology of $S^1$ and its subspace topology in Homeo$(S^{n+1})$?
- A sequence converges if and only if every subsequence converges?
- Tukey's lemma by axiom of choice
- Characterization of lower semicontinuous functions
- Constructing a bijection from (0,1) to the irrationals in (0,1)
- Why $f^{-1}(f(A)) \not= A$
- What means a “$\setminus$” logic symbol?
- The norm of a $d$-tuple of operators in Hilbert space
- In what way is the Peano curve not one-to-one with $^2$?
- A strange puzzle having two possible solutions

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.

- Evaluate accuracy of polynomial root finding
- How to solve $\mathrm dX(t)=B(t)X(t)\mathrm dt+B(t)X(t)\mathrm dB(t)$ with condition $X(0)=1$?
- Is empty set element of every set if it is subset of every set?
- A tricky infinite sum— solution found numerically, need proof
- Do all rational numbers repeat in Fibonacci coding?
- Ways to put $n$ balls into $m$ boxes
- Does $A=\{a|\forall x\in \emptyset\ H(x,a) \}$ make sense?
- How to find complex numbers $z,\lambda,\mu$ such that $(z^\lambda)^\mu\neq z^{\lambda\mu}$
- Proving an 'obvious' Ramsey upperbound
- Is there always an equivalent metric which is not complete?
- Induction proof error
- Krull dimension of quotient by principal ideal
- The fundamental group of $U(n)/O(n)$
- Books, Video lectures, other resources to Teach Yourself Analysis
- another balls and bins question