Coloring. Consider the infinite collection of circles below:
Suppose you have two markers, one red and one blue, and you color each circle one of the two colors. How many different ways can you color the circles? Do you think that the set of all possible circle colorings has the same cardinality as the set of all natural numbers? This question is tricky; just make a guess and explain why you guessed what you guessed (you need not rigorously justify your answer). You may first want to answer the question for just these four circles as a warm-up. We’ll return to this Mindscape later.
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