Question

state whether the following sets are finite or infinite

1. {x€R:x is a rational number}

2.{x€N:x is a rational number}​

Answer 1

Answer:

Take any random rational numbers(fractional) from 1 to 5. Denominators ur wish.

Step-by-step explanation:

Same procedure follows to N

A={(1/1), 1/2, 1/3,...}

So for both Infinite..

Answer 2

Both the sets {x ∈ R: x is a rational number} and {x ∈ N: x is a rational number}​ are infinite.

• In 'mathematics', 'rational numbers' are a special type of real numbers which can be represented as $\frac{p}{q}$, where p and $q(\neq 0)$ are two co-prime integers.
• Here in the question, R represents the set of 'real numbers' and N represents the set of natural numbers.
• The first set {x ∈ R: x is a rational number} represents all the real numbers that are also "rational numbers". We know that all rational numbers are real numbers. So this set actually represents all the "rational numbers". So the set is infinite.
• The second set {x ∈ N: x is a rational number} represents all the "natural numbers" that are also rational numbers. We know that all natural numbers are also rational numbers. So this set actually represents the set of "natural numbers". So this set is infinite.

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