Question

Let $(A_i\mid i\in I)$ be a family of disjoint sets where $|A_i|=|A_j|\ge\aleph_0\space\forall i\in I$. Is $|\bigcup\limits_{i\in I}A_i|=|A_i|$?

score 53 · Answer 1 · 2018-09-15 06:56:32

Let $(A_i\mid i\in I)$ be a family of disjoint sets where $|A_i|=|A_j|\ge\aleph_0\space\forall i\in I$. Is $|\bigcup\limits_{i\in I}A_i|=|A_i|$?

score 45 · Answer 2 · 2018-09-15 09:58:59

45

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List Question

Let $(A_i\mid i\in I)$ be a family of disjoint sets where $|A_i|=|A_j|\ge\aleph_0\space\forall i\in I$. Is $|\bigcup\limits_{i\in I}A_i|=|A_i|$?

Let $A$ be infinite and $\operatorname{Sq}(A)$ be the set of finite sequences in $A$. Then $A$ and $\operatorname{Sq}(A)$ are equinumerous

Integrals of $\int^\infty _2 \frac{x}{x^3 -2\sin x}dx$

Comparing the number of real numbers between 2 ranges

Analytical convergence of an equation?

What order of infinity is the set of vectors whose components sum to $0$?

Proving that $\tau = \{N,\varnothing\}\cup \{S_n:n\in\mathbf{N}\}$ is a topology on $\mathbf{N}$.

Prove that the summation from n=0 to infinity of a^n is 1/(1-a)

Using the Definition of Dedekind-Infinite to Replace the Axiom of Infinity

Computing $\lim_{x\to (3/2)^-} (x^2+1)/(3x-2x^2)$

Divergence of infinite series $(\frac{3k-2}{4k+2})^{2k-3}$

ZF + (Weak Axiom) $\vdash$ Dedekind Finite Implies Finite (Direct Proof)

Differentiating infinity wrt any variable: is it zero or undefined?

What is the difference between an infinite set of 1 dollar bills and an infinite set of 20 dollar bills?

Devils and Infinity

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