The exercise for today is to map the set of all positive integers into the space between zero one one … using my trusty version of set theory.
Since this space can be described by a set of rational numbers (1/4, 9/77, 17/209, etc. ), to map the infinite set of integers, we need to set the denominator of all these fractions to infinity. Then all integers easily map into the numerators of this set of rational numbers … as 1/infinity, 2/infinity, … ip to infinity/infinity .… and since any number divided by infinity equals zero … adding up the set of all these rational numbers (equivalent to zero) totals to the number value of one!
Perhaps this paradox can be resolved by positing that the last number in the above rational number set (infinity/infinity) is equal to one. Not very satisfying … but it works.
STAND UP FOR MATHEMATICS!
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