Question
Let A be a subset of [0,+).Assume that the sum of any finitenumber of elements inAis no greater than 1, i.e.,mN and a1, a2, ..amA,
Let A be a subset of [0,+).Assume that the sum of any finitenumber of elements inAis no greater than 1, i.e.,mN and a1, a2, ..amA, a1+a2+...am1.
Show thatAis countable.
And there is a hint:try to writeAas the union of a sequenceof finite sets.
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College Algebra Graphs and Models
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
5th edition
321845404, 978-0321791009, 321791002, 978-0321783950, 321783956, 978-0321845405
