MathematicsChapter 1: Real Numbers
Trichotomy and Inequality
Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once.
Learning objectives
- Define and explain trichotomy and inequality.
- Apply trichotomy and inequality to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once. Harriot ~1630 gave us the sharp signs < and >. If a < b and c > 0, then ac < bc (direction kept). If a < b and c < 0, then ac > bc (direction reverses). Adding the same number never flips the sign.
Where / symbols
- Trichotomy And Inequality
- Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once. Harriot ~1630 gave us the sharp signs < and >. If a < b and c > 0, then ac < bc (direction kept). If a < b and c < 0, then ac > bc (direction reverses). Adding the same number never flips the sign.
Overview
Learn the idea, then use it:
Core Understanding
Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once. Harriot ~1630 gave us the sharp signs < and >. If a < b and c > 0, then ac < bc (direction kept). If a < b and c < 0, then ac > bc (direction reverses). Adding the same number never flips the sign.
Examples Trichotomy · Harriot · 1630 · TRICHOTOMY AND INEQUALITY: Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once. Harriot ~1630 gave us
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — TRICHOTOMY AND INEQUALITY
Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once. Harriot ~1630 gave us the sharp signs < and >. If a < b and c > 0, then ac < bc (direction kept). If a < b and c < 0, then ac > bc (direction reverses). Adding the same number never flips the sign.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge trichotomy and inequality with a neighbouring idea that uses a different definition, rule, or method.
Key points
- Trichotomy
- Harriot
- 1630
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Trichotomy and Inequality
Sticky Notes · Quick Revision
Core Idea
- Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once.
Key Points
- Trichotomy
- Harriot
- 1630
Simple Check
- Explain trichotomy and inequality in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge trichotomy and inequality with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- Trichotomy: a sits left of b, on b, or right of b on the number line, never two of those at once.
- Trichotomy
- Harriot
- 1630
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