Pre-U Cambridge Further Mathematics: Essential Vocabulary & Terminology Guide | Pre-U Cambridge 进阶数学：词汇术语速记指南

📚 Pre-U Cambridge Further Mathematics: Essential Vocabulary & Terminology Guide | Pre-U Cambridge 进阶数学：词汇术语速记指南

Welcome to the ultimate vocabulary memorisation guide for Pre-U Cambridge Further Mathematics. A strong command of terminology and notation is crucial for interpreting questions and expressing solutions clearly. This article compiles key terms from the syllabus, each with a concise definition in English and Chinese, plus memory tips to help you recall them under exam pressure. Use it as a rapid revision tool alongside your past papers.

欢迎阅读 Pre-U Cambridge 进阶数学终极词汇速记指南。牢固掌握术语和符号对于理解题意和清晰表达解答至关重要。本文汇总了考纲中的核心术语，每个都配有中英文简明定义和记忆要点，帮助你在考试压力下迅速回忆。请结合历年真题将其用作快速复习工具。

1. Core Symbols & Set Notation | 核心符号与集合记法

ℕ (Natural Numbers): The set {1, 2, 3, …} sometimes including 0. Essential for indexing sequences and series.

ℕ（自然数）： 集合 {1, 2, 3, …}，有时包含 0。在数列和级数的下标中必不可少。

ℤ (Integers): All whole numbers, positive, negative and zero. Used widely in modular arithmetic and proofs.

ℤ（整数）： 所有正整数、负整数和零。广泛用于模运算和证明题。

ℚ (Rational Numbers): Numbers that can be expressed as a fraction p/q with p,q ∈ ℤ, q ≠ 0. Important for exact values.

ℚ（有理数）： 可以表示为 p/q 的数，其中 p,q ∈ ℤ，q ≠ 0。在精确值中很重要。

ℝ (Real Numbers): All numbers on the continuous number line. Pre-U calculus and modelling rely on ℝ.

ℝ（实数）： 数轴上所有连续的数。Pre-U 的微积分和建模都依赖 ℝ。

ℂ (Complex Numbers): The superset of ℝ containing all numbers of the form a + bi with i² = −1.

ℂ（复数）： 实数的超集，包含所有形如 a + bi 的数，其中 i² = −1。

∀ (For All) and ∃ (There Exists): Quantifiers. ‘∀ ε > 0’ means ‘for every positive epsilon’; ‘∃ δ > 0’ means ‘there is a positive delta’.

∀（任意）和 ∃（存在）： 量词。’∀ ε > 0′ 表示 ‘对任意正 ε’；’∃ δ > 0’ 表示 ‘存在正 δ’。

⇒ (Implies) and ⇔ (Equivalent): A ⇒ B: if A then B. A ⇔ B: A if and only if B. Master these for logical reasoning.

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