Classification of Real Numbers: Problems with Solutions

Natural numbers: $N=\left\{ 1,2,3,4,5,6,7,............\right\} $

Integers(whole numbers): $Z=\left\{......-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7.......\right\}$

Rational numbers: $Q=\left\{ ......-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7......\frac{3}{2},-\frac{1}{5},\frac{4}{3},....\right\}$

Irrational numbers: $I=\left\{ \sqrt{2},-\sqrt{5},e,\pi ....\right\} $. In the image R\Q represents the set of irrational numbers.

Real numbers: $R=Q\cup I$ - the real numbers are the union of rational and irrational.

Problem 1
Classify the numbers $\frac{7}{5}$, $0$, $-2.4$, $e+1$, $3\times 10^{6}$
Please, open the solution!
Problem 2
Which of the following statements is true?
Problem 3
Is it true that $3\in Z$?
Problem 4
Is it true that $-3\in N$?
Problem 5
Is it true that $\sqrt{2}\in Q$
Problem 6
$\frac{3}{4}$ is a rational number and $2$ is natural number. What kind of number is $\frac{3}{4}+2$?
Problem 7
Is the following statement true?
Every natural number is also an integer.
Problem 8
Is the following statement true?
Every natural number is also a rational number.
Problem 9
Is the following statement true?
Every irrational number can be written as a fraction.
Problem 10
Is it true that
$-2\in Q$?

Problem 11
Is it true that
$\pi \in I$?
Problem 12
How many of the following numbers are integers?
$0,$ $\frac{-4}{2},2^{3},\frac{5}{2},e,\sqrt{2},-\sqrt{9}$
Problem 13
Consider the number $n=\frac{3}{5}-2$
Which of the following statements is false?
Problem 14
If $m,n$ are rational numbers, which of the following statements is true?
Problem 15
Consider the number $3.25$ is either rational or irrational?
Problem 16
The number $n=2.151515151515.......$ has infinite decimals and $15$ repeats infinite number of times.
Is it rational or irrational?
Problem 17
Is the number $\frac{\sqrt{5}}{2}$ either rational or irrational?
Problem 18
Is the product of two rational numbers a rational number?
Problem 19
Is the product of two irrational numbers an irrational number?
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