MathDB

We define a relation between subsets of

\mathbb R ^n

A \sim B\Longleftrightarrow

we can partition

A,B

in sets

A_1,\dots,A_n

and

B_1,\dots,B_n

(i.e

\displaystyle A=\bigcup_{i=1} ^n A_i,\ B=\bigcup_{i=1} ^n B_i, A_i\cap A_j=\emptyset,\ B_i\cap B_j=\emptyset

) and

A_i\simeq B_i

. Say the the following sets have the relation

\sim

or not ? a) Natural numbers and composite numbers. b) Rational numbers and rational numbers with finite digits in base 10. c)

\{x\in\mathbb Q|x<\sqrt 2\}

and

\{x\in\mathbb Q|x<\sqrt 3\}

A=\{(x,y)\in\mathbb R^2|x^2+y^2<1\}

and

A\setminus \{(0,0)\}

Problem Statement