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Question: How to determine if a Set is infinite or Finite

Question:How to determine if a Set is infinite or Finite

Adam Ledger 360 Maple
set
June 08 2018
0

As an example question, I am trying to learn a method for assertaining whether a Set with a given predicate is finite or infinite.

 

For example, is $S$ infinite or finite, if it is defined as:

 

$$S={\biggl\{k \in \mathbb N:\biggl\lfloor {\frac {{k-1}}{{2}
}} \biggr\rfloor-\biggl\lfloor {\frac {{\ln(\pi^{k})}}{{\ln(10)}
}} \biggr\rfloor=0}\biggr\}$$
 
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