Cardinality and Infinity

⚠️ Warning: This material historically sent mathematicians to mental hospitals. Proceed with caution!

Quick Logic Note: Ex Falso Quodlibet

If P is false, then P ⇒ Q is always true, regardless of Q.

This is called ex falso quodlibet (Latin: "from falsehood, anything follows").

• Logic form: P ⇒ Q is logically equivalent to ¬P ∨ Q
• Example: "If I am a bee, then I will kill you" is logically TRUE (because I am not a bee)
• This is material implication in logic, not real-world causation

Visual Tests for Functions (Review)

Vertical Line Test

Tests if something is a function

• Draw vertical lines through the graph
• If any vertical line crosses the graph more than once → NOT a function
• One x-value cannot map to multiple y-values

Horizontal Line Test

Tests if a function is injective

• Draw horizontal lines through the graph
• If any horizontal line crosses more than once → NOT injective (monkeys sharing bananas)
• If every horizontal line crosses at most once → Injective

Surjectivity Test