Hi, I am the Foolish Philosopher. Today's video is part of the series Foolish Questions. These are somewhat silly questions which pop into my brain for no reason at all and to which I don't know the answer and perhaps has no answer but perhaps you know the answer. in which case I would encourage you to pop the answer into the comment section below or perhaps leaving an insight or further questions on this topic or a totally unrelated topic. Here is today's question.
Let’s say we had two rectangles. Rectangle A has a width of X and rectangle B has a width of 2X. Both rectangles have a length of infinity. Is it possible to
measure the area for either rectangle and
prove that rectangle B is larger than rectangle A or vice versa?
Perhaps a bonus question might be what effect would X being a negative integer have upon the rectangles and the comparative relationship between rectangles. Essentially the question is can various degrees of infinity manifest in reality. If you take the set of counting numbers comparatively against the set of odd numbers is one infinite set greater than the other? Intuitively it seems one is larger and yet they are both the same. How can we be sure of this?
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To quote William Shakespeare “A fool thinks himself to be wise, but a wise man knows himself to be a fool.”