Why Can't You Multiply Vectors? Exploring the Math behind Games

🧮Natural numbers are closed under addition and multiplication, but not subtraction or division.

➖Integers include negative numbers and are closed under addition, subtraction, and multiplication.

➗Rational numbers are obtained from division of integers and are closed under addition, subtraction, multiplication, and division.

√Real numbers extend from rational numbers and include numbers like square roots that can't be expressed as fractions.

❓Exploring the next step: Complex numbers, which extend from real numbers and include imaginary components.

Why can't natural numbers be obtained through subtraction?

—Subtraction of natural numbers can result in negative numbers, which are not considered natural numbers.

What is the difference between rational and real numbers?

—Rational numbers can be expressed as fractions, while real numbers include numbers like square roots that can't be expressed as fractions.

What operations are closed under rational numbers?

—Rational numbers are closed under addition, subtraction, multiplication, and division.

What is the next step beyond real numbers?

—The next step beyond real numbers is complex numbers, which include imaginary components and extend from real numbers.

What are the applications of these different types of numbers in game development?

—These different types of numbers are used in various mathematical operations and calculations within game development, such as physics simulations, graphics rendering, and procedural content generation.

00:00Introduction to the topic of understanding the math underlying games and the inability to simply multiply vectors.

09:23Explanation of natural numbers and their closure under addition and multiplication, but not subtraction.

11:20Introduction to integers, which include negative numbers and are closed under addition, subtraction, and multiplication.

13:39Introduction to rational numbers obtained through division of integers and their closure under all basic operations.

15:16Introduction to real numbers, which extend from rational numbers and include numbers like square roots.

18:00Mention of the next step beyond real numbers, which is complex numbers with imaginary components.

19:54Application of these different types of numbers in game development, such as physics simulations, graphics rendering, and procedural content generation.