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mathmath333 one year ago set theory

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1. mathmath333

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}}

2. welshfella

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

3. ikram002p

well lets try each one condition solution :)

4. ikram002p

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

5. ikram002p

in which way this confuses u @mathmath333 ??

6. mathmath333

prove that an empty set is finite set

7. ikram002p

awww thats so cute question :P

8. ikram002p

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.

9. mathmath333

does empty set has a subset

10. ikram002p

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

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