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反例证明与命题判断

反例证明与命题判断
几何画板及绘图内容加载中，请稍等……
2015-11-22 22:33
概率统计几何作图
本范例演示如何通过 GeoGebra 提供反例来推翻数学命题。涉及的核心数学概念包括逻辑推理与命题真值判断。作图要点运用了 LaTeX 命令、角落标记 Corner、步进器 stepper、最大步进 stepMax、步骤 steps、反例 counter、点 A 和 B、x 和 y 轴范围控制 xmin, xmax, ymin, ymax、按钮 button1 以及多个文本框 text1 至 text8。适合高中数学逻辑与证明教学，帮助学生理解反例在数学证明中的作用。

GeoGebra 命令及参数

  1. LaTeX(steps) → counter
  2. Corner(1) → A
  3. Corner(3) → B
  4. LaTeX("\text{Determine a counterexample.}") → text1
  5. LaTeX("\text{A counterexample is an example that disproves the conjecture.}") → text2
  6. LaTeX("\text{Think of an example of a person who lives in America but is not an American.}") → text3
  7. LaTeX("\text{A Korean foreign-exchange student would be an example of someone who lives in}\cr\text{America but is not an American.}") → text4
  8. LaTeX("\text{Determine the truth value of the original conjecture.}") → text6
  9. LaTeX("\text{Since a counterexample was found, this means that there is at least one example}\cr\text{where this statement is not true.}") → text7
  10. LaTeX("\text{Therefore, the statement “If a person lives in America, then he or she is an}\cr\text{American” is false.}") → text8
  11. LaTeX("\text{Move the slider to solve the problem.}") → text0
  12. LaTeX("\text{A Korean foreign-exchange student is a counterexample for the conjecture}\cr\text{“If a person lives in America, then he or she is an American.”}") → text5
  13. LaTeX("\text{“If a person lives in America, then he or she is an American.”}") → Problem