maths

• Deductive reasoning:

  • Method of proving a theory or hypothesis using formal logic and observations
  • Starts with a hypothesis that is supported or disproved through observations or rational thought
• Inductive reasoning:

  • Employs theories and assumptions to validate observations
  • Requires deducing a general rule from a specific case or cases
  • Outcomes are not always certain, used for extrapolation, forecasts, and part-to-whole arguments
• Analogical reasoning:

  • Looks for similarities between objects and uses those similarities to find other shared properties
  • Based on the brain's tendency to notice patterns and make connections
• Abductive reasoning:

  • Reaches a logical conclusion based on an observation or group of observations
  • Allows making the greatest estimates to get the simplest conclusions
  • Helps with troubleshooting and decision-making, especially in uncertain situations
• Cause-and-effect reasoning:

  • Demonstrates the relationship between two events
  • Used to describe potential outcomes of actions or reasons for events based on circumstances
  • Frequently used in daily decision-making and problem-solving
• Critical thinking:

  • Involves delving deeply into a topic's rationale to reach a definitive conclusion
  • Beneficial in computing, engineering, social sciences, and logic
  • Important for problem-solving, especially in technological challenges
• Decompositional reasoning:

  • Process of breaking things down into basic components to understand how each contributes to the overall functionality
  • Allows deriving powerful conclusions about the total by evaluating each portion separately