Question

1. causation
2. sequence
3. term
4. arithmetic sequence
5. common difference
6. piecewise function
7. step function

Explanation:

Definitions for each mathematical term are provided below, aligned with standard academic definitions.

1. Causation: A relationship where one event directly causes another; a change in one variable produces a measurable change in another, distinct from correlation.
2. Sequence: An ordered list of numbers/objects following a pattern.
3. Term: An individual element in a sequence/mathematical expression.
4. Arithmetic Sequence: A sequence with a constant difference between consecutive terms.
5. Common Difference: The constant value between consecutive terms in an arithmetic sequence, denoted $d$.
6. Piecewise Function: A function defined by multiple sub-functions, each applying to a specific interval of the domain.
7. Step Function: A piecewise constant function with finite, constant values over intervals, forming "steps" on a graph.

Answer:

1. Causation: A relationship where one event directly results in another event; a change in one variable directly induces a change in another (not just a correlated relationship).
2. Sequence: An ordered list of numbers, objects, or terms that follow a specific pattern or rule.
3. Term: A single element, number, or expression within a sequence, series, or mathematical equation.
4. Arithmetic Sequence: A sequence of numbers where the difference between consecutive terms is a constant value.
5. Common Difference: The fixed, constant value that is added to each term in an arithmetic sequence to get the next term, represented as $d$.
6. Piecewise Function: A function that is defined by multiple distinct sub-functions, each of which applies to a separate, specific interval of the function's domain.
7. Step Function: A type of piecewise function that has a constant value over each interval of its domain, creating a graph that looks like a series of horizontal "steps".