In this problem we are laying out a walkway with slate tiles in 3 different colo

Question

In this problem we are laying out a walkway with slate tiles in 3 different colours. The colours are yellow, red and blue. The length of a walkway is the number of tiles in the walkway. (An example of a walkway of length 5 is Red, Blue, Red, Yellow, Blue. )

Let us now consider th e set S which contains all INFINITELY long walkways. Is the set S countable?

Explain your reasoning! If you believe that the set is countable, then you must show how we can list the elements as number 1, 2, 3 etc. If not, then you must prove t hat the set is uncountable.   

Explanation / Answer

It is not countable.

The term INFINITELY long means longer than you can imagine.It doesn't matter how much large number you think you can simply add a 1 and get to see a bigger number than you have imagined.More specifically Infinity is actually not a number it is a concept of the largest number(where there is no end).

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