P2.1

• Language


  A systematic means of communicating by the use of sounds or conventional symbols
• Mathematical language


  A system used in the field of mathematics to communicate mathematical ideas, concepts, and theories among people
• Characteristics of mathematical language

  • Concise- Able to say things briefly
  • Powerful- Able to express complex thoughts with relative ease
  • Precise - able to make fine distinctions
• The language of mathematics was designed for numbers, sets, functions, and performing operations
• Context


  The particular topics being studied
• Convention


  A fact, name, notation or usage which is generally agreed upon by many mathematicians
• Conventions in mathematics


  • Capital letters used to name a dot or set and label vertices of a polygon
  • Always express fractions in the simplest form
  • Constructing a Venn diagram: represent universal set using a rectangle and various sets of objects using circular regions including those regions formed by intersection circles
  • Use the name of the definition, postulate or theorem instead of writing its content
  • Distances in a coordinate system are non-negative
• Mathematical symbols


  Used to refer to certain quantities, concepts, and ideas
• Common mathematical symbols


  • ∩, ∪, ⊂, ⊃ (Sets)
  • +, -, ×, ÷ (Operations)
  • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (The ten digits)
  • a, b, c, x and y (Variables)
  • =, ≠, ≈, <, >, ≤, ≥, π (Special symbols)
  • ~, ^, v, →, ↔ (Logic symbols)
  • N, W, Z, Q, R, C (Set Notations)
• Mathematical expression


  A finite combination of symbols that is well-formed according to rules that depend on the context
• Mathematical sentence


  A sentence that can be identified as either true or false