Question

set theory

Answer 1

State which of the following sets are finite or infinite :
\(\large \color{black}{\begin{align}& (i)\ \{x : x \in \mathbb{N} \ \ and \ \ (x – 1) (x –2) = 0\} \hspace{.33em}\\~\\
& (ii)\ \{x : x \in \mathbb{N} \ \ and \ \ x^{2} = 4\} \hspace{.33em}\\~\\
& (iii)\ \{x : x \in \mathbb{N} \ \ and \ \ 2x –1 = 0\} \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

sorry I've done this stuff in the past but i cant recall it well enough.

Answer 3

well lets try each one condition solution :)

Answer 4

to me i and ii are finite and iii is Empty which is also finite

Answer 5

in which way this confuses u @mathmath333 ??

Answer 6

prove that an empty set is finite set

Answer 7

awww thats so cute question :P

Answer 8

i have many proves the most lovely one is using this :-
there are infinite subsets of an infinite set
and there are finite subsets of a finite set.

thus subsets of an Empty set is ( 2^0=1) which is finite QED.

Answer 9

does empty set has a subset

Answer 10

yes it does have 1 subset which is also an empty set (itself only)