Answer to Question #132585 in Discrete Mathematics for Ankita

Question #132585
Prove that 3Z is an infinite set
1
Expert's answer
2020-09-14T13:34:19-0400

We known that Z={...,3,2,1,0,1,2,3,...}\Z = \{ ... , - 3,-2,-1,0,1,2,3, ... \} .

Hence, 3Z=3×{...,3,2,1,0,1,2,3,...}={...,9,6,3,0,3,6,9,...}3\Z = 3 \times\{ ... , - 3,-2,-1,0,1,2,3, ... \} = \{ ... , - 9,-6,-3,0,3,6,9, ... \} .

By completeness property of real numbers, for every kRk \in \R ,  nZ:nk\exist \ n \in \Z : n \geq k . Hence, Z\Z is an infinite set.


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