Lecture Notes: Mathematical Terminologies and Classifications

Key Terminologies

• Nth Root of A:
  • Order/Index: The value of N when taking the nth root (e.g., order of cube root is 3).
  • Radical: The root sign (√) used in mathematical notation.
  • Radicand/Base: The number under the radical.
• SERD:
  • Defined as the irrational root of a positive rational number.
  • Examples: √3 (square root of 3), ³√5 (cube root of 5).
  • Non-examples: √4, ³√8 (result in rational numbers).

Classification of Real Numbers

• Types of Real Numbers:
  • Rational Numbers: Numbers that can be expressed as a fraction of two integers.
  • Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers.

Subcategories within Irrational Numbers

• Irrational Numbers Examples:

  • √2, ³√7, √5 (typical irrational numbers from roots).

• Special Irrational Numbers (CERDS):

  • Definition: Specifically, irrational roots of positive rational numbers.
  • Examples:
    • Numbers like π (pi) and e (Euler's number) are not CERDS.
  • Misconception: Not all irrational numbers are CERDS; only irrational roots of positive rational numbers qualify.

Summary

• Understanding the distinction between different types of numbers and the specific categorization of CERDS is essential in mathematics.
• CERDS specifically refer to irrational outcomes of roots from positive rational numbers, not to be confused with other irrational numbers like π and e.