Teaching-mechanic library

reverse_factory · math · transformer.inverse

Concept: Inverse functions

Player does: Run the machine backward to recover the input

Breaks: f⁻¹(x) means 1/f(x)

The inverse function f⁻¹ undoes f by swapping inputs and outputs; it is not the reciprocal 1/f(x).

input_filter · math · transformer.domain_filter

Concept: Domain & range

Player does: Choose which crates the √ or 1/x machine accepts without jamming

Breaks: Every real number is a valid input

A function's domain excludes inputs that break it, like negatives under a square root or zero in a denominator.

transform_key · math · transformer.geometric

Concept: Rigid transformations & symmetry

Player does: Rotate, reflect, translate the key until it fits the slot

Breaks: A line reflection equals a 180° rotation

A reflection flips a shape's orientation while a 180° rotation preserves it, so the two are not the same transformation.

closing_walls · math · function_world.squeeze

Concept: Squeeze theorem

Player does: Upper and lower walls close in; predict where the trapped orb ends

Breaks: The trapped function can escape between the bounds

If two bounding functions converge to the same limit, the squeezed function trapped between them must converge there too.

precision_zone · math · function_world.epsilon_delta

Concept: ε-δ definition

Player does: The target band shrinks; choose how close x must stay to a

Breaks: You pick δ first, then ε

The ε-δ definition works the other way: for any tolerance ε chosen first, a matching δ must be found.

transformation_grid · math · transformer.matrix

Concept: Matrices as transformations

Player does: Pick the 2×2 matrix that turns the rune into the door's shape

Breaks: Matrix multiplication is commutative

Matrix multiplication generally is not commutative, so applying two transformations in a different order gives a different result.

determinant_press · math · transformer.matrix

Concept: Determinant as area scale

Player does: Predict the stamped area after the matrix press

Breaks: The determinant is the sum of the entries

The determinant measures how a matrix scales area (or volume); it is computed from a product-and-difference formula, not a sum of entries.