GE 112: Math Language and Symbols Module 2

Study Notes

Mathematical Language

Understanding mathematical language is essential for grasping mathematical ideas, as the concepts can often seem foreign without proper terminology.
It is a system of communication that deals with objects like numbers, variables, sets, operations, functions, and equations.
Mathematics has its own specialized vocabulary, grammar, and syntax.

Characteristics of Mathematical Language

Precision: Enables the articulation of very fine distinctions in thought.
Conciseness: Allows for expressions to be made brief and to the point.
Powerfulness: Capable of articulating complex ideas with relative ease.

Mathematical Symbols and Notations

Common operational symbols include:
- Addition: +
- Subtraction: −
- Multiplication: ×
- Division: ÷
Symbols representing values typically include letters such as:
- a, b, c, x, y, z, etc.

Number Sets and Their Symbols

N: Set of natural numbers {1, 2, 3, 4,...}
W: Set of whole numbers {0, 1, 2, 3, 4,...}
Z: Set of integers {..., −2, −1, 0, 1, 2,...}
R: Set of real numbers (−∞, ∞)
Q: Set of rational numbers {ab : a, b ∈ Z ∧ b ≠ 0}
QC: Set of irrational numbers {x | x is a nonrepeating and nonterminating decimal}
C: Set of complex numbers {x + iy : x, y ∈ R, i² = −1}

Logical Symbols

∧: Represents logical "and"
∨: Represents logical "or"
∈: Indicates an element of a set
/∈: Indicates not an element of a set
→: Symbolizes "if - then"
↔: Represents "if and only if"
∀: Means "for any" or "for all"
∃: Signifies "there exists" or "there is"
∴: Symbolizes "therefore"
∩: Represents intersection
∪: Represents union

Description

Explore the fundamental aspects of mathematical language and symbols in this module for GE 112: Mathematics in the Modern World. Topics covered include elementary logic, sets, and the foundations of mathematical expression. Enhance your understanding and application of mathematical terminology.