📝 Set Representation
A Set is a well-defined collection of distinct objects. Let's look at a basket of fruits. We can represent this set in different ways.
Our Fruit Set F
Lists all elements clearly separated by commas inside curly braces.
U Universal Set
The Universal Set (U or ε) contains all possible elements under consideration. Every other set we discuss is a subset of the Universal Set.
Universal Set (U)
The entire grocery store inventory of fruits.
{ 🍎, 🍊, 🍋, 🍌, 🍇, 🍓, 🍉 }
Set C (Citrus)
{ 🍊, 🍋 }
Set Y (Yellow Fruits)
{ 🍌, 🍋 }
∅ The Empty Set
A set that contains no elements is called the empty set or null set. It is denoted by ∅ or {}. Try filtering the basket below.
All fruits in our basket.
∞ Finite vs Infinite Sets
A Finite Set has a specific, countable number of elements. An Infinite Set continues endlessly.
Finite Set
CountableSet A = { Fruits currently in my bowl }.
We can easily count them. There are exactly 4.
Infinite Set
Set N = { Natural Numbers }.
Imagine picking a fruit, tagging it with a number, forever.
⊆ Subsets
Set A is a subset of Set B (A ⊆ B) if every element in A is also in B. Build Set A by clicking fruits below!
Target Set B (The Standard Basket)
Click to add to your Set A:
Add some fruits to check if it's a subset!
P(S) Power Set
The Power Set P(S) is the set of all possible subsets of S, including the empty set and S itself. If S has n elements, P(S) has 2n elements.
Build Set S (Max 3 items)
Results: P(S)
Size: 2⁰ = 1 subsets⋃ Set Operations
Let's look at operations like Union, Intersection, and Complement. We will use a practical example of 10 Animals at a rescue center as our Universal Set U.
Choose Operation:
Click a button above to see the result and visual representation.
Climbers
Long Tails