lesson
Updated 6 days ago · 2 views
Think about your own address: you live in a specific room, inside a house, inside a city, inside a country. A single location belongs to multiple bigger groups all at once.
Numbers work the exact same way. Depending on how they look and behave, numbers belong to nested categories called sets.
How do these number groups fit inside each other?
The Three Main Sets
We organize everyday numbers into three nested groups: whole numbers, integers, and rational numbers.
📊A clean nested Venn diagram / set diagram with 3 concentric rounded rectangles or ovals on a light background (#f8f9fa). Innermost circle: 'Whole Numbers' (light green #e8f5e9, border #4caf50) containing '0, 1, 4, 100'. Middle ring enclosing the whole numbers: 'Integers' (light blue #e3f2fd, border #2196f3) containing '-3, -12, -50'. Outer ring enclosing all: 'Rational Numbers' (light purple #f3e5f5, border #9c27b0) containing '1/2, -3.75, 0.333..., -7/8'. Clear labels for each layer, responsive down to 350px width, text color #1e2945.
Because the circles sit inside one another, every whole number is automatically an integer, and every integer is automatically a rational number.
What makes a number belong to the very center of the diagram?
Whole Numbers and Integers
Whole numbers are the counting numbers starting at zero: 0,1,2,3,… with no fractions, decimals, or negative signs.
Integers expand this group by adding negative opposites, giving us all positive and negative whole values: …,−3,−2,−1,0,1,2,3,….
For example, −7 is an integer but not a whole number, while 7 is both a whole number and an integer.
What happens when we split numbers into parts and pieces?