Then you start placing your "bushels" along diagonals of increasing size, see wikipedia. Perhaps surprisingly the answer is yes! You make the rational numbers into a big square grid with the numerator and denominators as the two coordinates. Can you do so in a way that gets all of my rational numbers? So suppose you have the set of positive integers and I have the set of rational numbers and you want to trade me one positive integer for each of my rationals. We can try doing the same thing with infinite sets. We've just proved that the number of sheep is the same as the number of bushels without actually counting. That's just fancy language for saying you pair things up by putting one bushel next to each of the sheep. We form a "bijection" between the two sets. But there's a problem, we don't know how to count the bushels or the sheep! So what do we do? Then suppose that you and I agreed that we would trade one bushel of corn for each of my sheep. Suppose no one ever taught you the names for ordinary numbers.
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