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

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

Maple

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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