Title: InkMaths / Key definitions
On every note of this deck, unless a note says otherwise:
Footer: Continue on InkMaths · © 2026 InkMaths. All rights reserved.

Front: DEFINE
Define: increasing function on an interval.
Back: One whose outputs follow the order of its inputs: for x₂ beyond x₁ in the interval, f(x₂) is at least f(x₁), and strictly increasing means always greater. Say which you mean, then test it: f'(x) ≥ 0 throughout gives the first, f'(x) > 0 the second.

Front: CHECK YOURSELF
A geometric series converges. State the condition on the common ratio, and the sum to infinity.
Back: Convergence needs |r| < 1, and then the sum to infinity is a/(1 − r).

Front: DEFINE
Define: counterexample.
Back: A single specific case for which a general statement fails, which is enough to disprove the statement.

Front: DEFINE
Define: arithmetic sequence.
Back: A sequence in which the difference between consecutive terms is constant, the common difference d.

Front: DEFINE
Define: geometric sequence.
Back: A sequence in which the ratio between consecutive terms is constant, the common ratio r.

Front: DEFINE
Define: radian.
Back: The angle subtended at the centre of a circle by an arc equal in length to the radius.

Front: DEFINE
Define: function.
Back: A mapping that sends every element of the domain to exactly one output. Two inputs may land on the same output. One input may never have two.