FUNDAMENTALS
The axiomatic structures of algebra: defining the number sets, the strict grammar of operations, and the power of the variable container.
01 // The Real Number System
Domain: ℝ
ℝ Real Numbers
ℚ Rationals
Ex: 1/2, 0.75, -5
ℤ Integers
Ex: ...-2, -1, 0, 1, 2...
ℕ Natural
1, 2, 3...
Irrational
π
Non-terminating,
Non-repeating decimals.
Non-repeating decimals.
02 // Order of Operations
Strict Hierarchy
Mathematics is not read strictly left-to-right like text. Expressions are parsed and evaluated by mathematical rank using the PEMDAS architecture.
1
Parentheses ( )2
Exponents x²3
Mult/Div × ÷4
Add/Sub + -Interactive Lab
Operation Deconstructor
Click the next step
Multiply before you Add.
03 // The Variable
x
Container
A Box for Value
A variable is not a specific, permanent letter; it is a conceptual bucket. It holds a number we don't know yet, or a number that changes depending on the situation. Evaluating an expression simply means "pouring" a known number into the bucket and running the math.
Execution Trace
Let x = 5
Evaluate: 2x + 3
2(5) + 3 = 13
Verification Protocol
Knowledge Check: Logic & Syntax1 / 3
Match the Real Number category to its correct example.
1. Select Term
2. Assign Match
Foundations Secured
You are ready to map variables to visual space.