Finding Intersections of Set A with Real, Rational, Integer, and Irrational Number Sets

Published on September 27, 2026

Algebra

Determine the intersections of the given set A containing square roots, pi, repeating decimals, and fractions with standard number systems such as R, Q, Z, I, and N.

Question

Answer

Based on the image provided, the set

is defined as:

First, let’s simplify and categorize the elements of

(Integer , Rational )
(Irrational )
(Irrational )
(Repeating decimal Rational )
(Rational )
(Non-repeating decimal Irrational )

Now, we find the intersections of

with the standard number sets (

: Reals,

: Rationals,

: Integers,

: Irrationals,

: Natural numbers):

Step 1: Intersection with Real Numbers ()
Since all elements are real numbers:

Step 2: Intersection with Rational Numbers ()
The rational numbers are those that can be written as a fraction:

Step 3: Intersection with Integers ()
Only

is an integer:

Step 4: Intersection with Irrational Numbers ()
The irrational numbers are the non-repeating, non-terminating decimals:

Step 5: Intersection with Natural Numbers ()
There are no positive integers or zero in the set:

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