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Real Numbers List the elements of the given set that are

(a) natural numbers

(b) integers

(c) rational numbers

(d) irrational numbers

 

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Joram Guingguing
Joram GuingguingLv10
23 Dec 2020

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4 Jan 2021

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DISCOVER PROVE: Combining Rational and Irrational Numbers

Is rational or irrational? is rational or irrational? Experiment with sums and products of other rational and irrational numbers. prove the following.

(a) The sum of a rational number r and an irrational number t is irrational

(b)The product of a rational number r and an irrational number t is irrational

[Hint: for part (a), suppose that r + t is a rational number q, that is r + t = q. Show that this leads to a contradiction. Use similar reasoning for part (b)]

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