HW Then B has upward closure Rational numbers themselves can be represented by t
ID: 1720200 • Letter: H
Question
HW Then B has upward closure Rational numbers themselves can be represented by two cuts... I can put the number itself in A or B, so consider cuts that differ by one rational to represent the same (rational) real. Its relatively easy to define addition and multiplication of cuts that works the way you would hope) and to check the ring axioms. Then reals are grounded in rationals which are grounded in integers which are grounded in counting numbers...and that's the only a priori notion. P(A) is a larger set than A reals In particular N (counting numbers) is smaller than P(N) same size as Does there exist any set of reals so small that you can't match it with the reals but so big you can't match it with the counting numbers?Explanation / Answer
As the set of irrational numbers are uncountable, so they can not be matched wwith the counting numbers,
Also since there are infintley many rational, so set of irrational can not be matched with the reals.
Hence the required set is set of irrationals.
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