QUESTION 1 [Properties of Numbers] |7| 1.1 From the lise of numbers: $$ -3: \frac{3}{4}: \sqrt{2}: \sqrt{9}: 0: 2: \sqrt{-4} \cdot $$ write down all the 1.1.1 Natural numbers 1.1.1 whole numbers 1.1.3 integers 1.1.4 rational numbers 1.1.5 irrational numbers 1.2 Between which two positive integers do the following irrational number lies? (2)

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### 1.1 List of Numbers
The given list of numbers is:
- $$ -3 $$
- $$ \frac{3}{4} $$
- $$ \sqrt{2} $$
- $$ \sqrt{9} $$
- $$ 0 $$
- $$ 2 $$
- $$ \sqrt{-4} $$

### 1.1.1 Natural Numbers
Natural numbers are the set of positive integers starting from 1. In this case, the natural numbers from the list are:
- $$ 2 $$

### 1.1.2 Whole Numbers
Whole numbers include all natural numbers and zero. From the list, the whole numbers are:
- $$ 0 $$
- $$ 2 $$

### 1.1.3 Integers
Integers include all whole numbers and their negative counterparts. The integers from the list are:
- $$ -3 $$
- $$ 0 $$
- $$ 2 $$

### 1.1.4 Rational Numbers
Rational numbers are numbers that can be expressed as a fraction of two integers. The rational numbers from the list are:
- $$ -3 $$ (can be expressed as $$ \frac{-3}{1} $$)
- $$ \frac{3}{4} $$
- $$ 0 $$ (can be expressed as $$ \frac{0}{1} $$)
- $$ 2 $$ (can be expressed as $$ \frac{2}{1} $$)

### 1.1.5 Irrational Numbers
Irrational numbers cannot be expressed as a fraction of two integers. The irrational numbers from the list are:
- $$ \sqrt{2} $$

Note: $$ \sqrt{9} = 3 $$ is a rational number, and $$ \sqrt{-4} $$ is not a real number (it's imaginary).

### 1.2 Between Which Two Positive Integers Does the Following Irrational Number Lie?
We need to determine between which two positive integers the irrational number $$ \sqrt{2} $$ lies.

Calculating $$ \sqrt{2} $$:
- $$ \sqrt{2} \approx 1.414 $$

The two positive integers between which $$ 1.414 $$ lies are:
- $$ 1 $$ and $$ 2 $$

### Summary of Answers
1.1.1 Natural numbers: $$ 2 $$  
1.1.2 Whole numbers: $$ 0, 2 $$  
1.1.3 Integers: $$ -3, 0, 2 $$  
1.1.4 Rational numbers: $$ -3, \frac{3}{4}, 0, 2 $$  
1.1.5 Irrational numbers: $$ \sqrt{2} $$  
1.2 Between which two positive integers does $$ \sqrt{2} $$ lie: $$ 1 $$ and $$ 2 $$
Natural numbers: 2 Whole numbers: 0, 2 Integers: -3, 0, 2 Rational numbers: -3, 3/4, 0, 2 Irrational numbers: √2 √2 lies between 1 and 2

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