Number System / संख्या प्रणाली Class 01 | Daftar Series for SSC CGL 2026 | By Aditya Ranjan Sir 🔥

Main ideas / lessons conveyed

• SSC/CGL-focused Number System (Class 01): The instructor frames the session as the beginning of a structured “Daftar” series to prepare for SSC (and also mentions other exams like Railways, UPSSSC, CHSL, CPO).
• “Number system” is broader than unit digits and divisibility tricks: The talk repeatedly distinguishes school-level fragments (e.g., unit digit, divisibility by 3/5, etc.) from the actual classification of number sets asked in exams.

Hierarchy of number sets (with “sons” metaphor)

• Complex numbers: written as (a + ib)
  • Real part: (a)
  • Imaginary part: (ib) (where (i^2 = -1))
• Real numbers: split into
  • Rational numbers
  • Irrational numbers
• Rational numbers: can be expressed in the form ( \frac{p}{q} ) with (q \neq 0)
  • Integers (no fractions)
  • Fractions (numerators/denominators present)
• Integers split into:
  • Whole numbers / “Wool” (non-negative integers including 0)
  • Negative integers
• Natural numbers: described as starting from 1 and going to infinity
  • Some discussion on where 0 fits in “whole” vs “natural”.

Rational vs Irrational via decimal behavior

• Rational: decimals are either
  • terminating, or
  • non-terminating but repeating
• Irrational: decimals are
  • non-terminating and non-repeating

Common exam confusion addressed

• 0 is a special case: discussed as neither positive nor negative (neutral).
• Example-based clarification
  • ( \sqrt{2} ) is used as an irrational example.
  • Expressions that look irrational but become rational after simplification are discussed to prevent misclassification.
• (\pi) is treated as irrational (decimal never terminates/repeats), while ( \frac{22}{7} ) is rational (used as an approximation in some exam problems).

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Methodology / learning plan (instructional flow)

• Session structure (as promised by the instructor)

  • The number system series has three classes:
    1. Classification of numbers (emphasis + many practice questions)
    2. Prime numbers / unit digits / factors (and related properties)
    3. Divisibility / remainders (and similar concepts)
  • The instructor also notes:
    • Practice-format questions after teaching (mentions 10 practice questions after instruction in the first class).
    • PDFs will be provided for notes/practice.

• How to study / practice

  • Do chapter-wise preparation first (don’t wait only for mock tests).
  • Use practice sets regularly:
    • Starting late can become a self-confidence issue (“negative about yourself”).
    • Mock tests should come later (e.g., near exam days).
  • Separate practice sets are mentioned for:
    • CGL
    • UPSC/UP (exact naming is unclear due to subtitle errors)

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Detailed bullet list of classification rules taught (core “number set” concepts)

1) Complex numbers

• Form: (a + ib)
• Components:
  • Real part: (a)
  • Imaginary part: (ib)
• Key exam idea: complex numbers are a superset; they’re not “the same” as real numbers.

2) Real numbers

• Real numbers are those representable on the number line.
• Split into:
  • Rational
  • Irrational

3) Rational numbers

• Can be written as: ( \frac{p}{q} ) where:
  • (p, q) are integers
  • (q \neq 0)
• Rationality implications for decimals:
  • Decimal is terminating OR repeating

4) Irrational numbers

• Cannot be written as ( \frac{p}{q} )
• Decimal behavior:
  • non-terminating and non-repeating
• Common example:
  • ( \sqrt{2} \approx 1.414…) (irrational)

5) Integers

• Integers are numbers with no fractional part:
  • negative integers, positive integers, and 0
• Decimal concept:
  • Not written as (p/q) with a non-1 denominator (in simplified form).

6) Whole numbers vs Natural numbers (as described)

• Whole numbers (“Wool” in subtitles): 0 and positive integers
• Natural numbers: 1, 2, 3, … to infinity
• 0’s classification:
  • treated as neutral (neither positive nor negative)

7) Relationship of sets (what is a subset of what)

From the instructor’s hierarchy:

• Natural ⊂ Whole ⊂ Integers
• Integers ⊂ Rational
• Rational ⊂ Real
• Irrational ⊂ Real
• Real ⊂ Complex

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Practice / question-solving concepts demonstrated

(The video contains many examples; subtitles are error-prone, but the recurring question types are clear.)

• MCQ-style set membership

  • Identify which group is not a subset of real numbers (complex is implied as the one that is not a subset of reals).
  • Determine what the real numbers include (rational + irrational).
  • Find a number that is real but not rational.

• Number line interpretation

  • “What does each point represent?”
  • Mapping sets (natural/rational/real) to regions on the number line.

• Operations / behavior across rational & irrational

  • The instructor discusses how results can vary when adding/multiplying/subtracting/dividing:
    • rational op rational → rational
    • irrational op irrational → can be rational or irrational
    • rational op irrational → can be rational or irrational (depends on operation and specific values)
  • Example-driven:
    • If irrational values cancel (e.g., (x + (-x))), the result can become 0 (rational).

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Key “decimal expansion” rules taught (terminating vs repeating)

• Terminating decimal → rational
• Non-terminating repeating decimal → rational
• Non-terminating non-repeating decimal → irrational

Pure recurring vs mixed recurring

• Pure recurring: repeating pattern starts immediately after the decimal point
• Mixed recurring: repeating pattern starts after some non-repeating digits

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Sources / speakers featured

• Speaker / Instructor: Aditya Ranjan Sir (referred to as “Guruji” / “sir”)
• Other individuals mentioned (students/winners/people congratulated):
  • Mishra ji / Mishra (and “madam”) (mentioned as associated persons; not clearly a separate full speaker on screen)
  • Several learners are name-dropped in subtitles (e.g., Yuvraj Singh, plus other winner/commenter names not fully captured due to subtitle errors)
• Organizations/exam boards referenced:
  • SSC (CGL, CHSL, CPO), Railways, UPSSSC/UP, UPSC/CS(E)T (exact names sometimes garbled)