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Ordering Real Numbers

Ordering Real Numbers
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2020-04-11 00:15
FunctionCalculus
This example demonstrates the ordering and visualization of real numbers. It involves core mathematical concepts such as real numbers, number line, inequalities, and upper and lower sums (Riemann sums). Construction highlights include using GeoGebra commands like Sequence, Segment, and Slider Animation to showcase sequence variations. Suitable for high school mathematics education, helping students understand real number properties and integral concepts.

GeoGebra Commands & Parameters

  1. Sequence(Random[5, 95] / 10, i, 1, 5) → list7_1
  2. Sequence(RandomElement[dens], i, 1, 5) → list6_1
  3. Sequence(Element[list7, i], i, 1, 5) → flist
  4. Sequence((-x(Element[list8, i])) + Element[flist, i] > error, i, 1, 5) → toosmall
  5. Sequence(x(Element[list8, i]) - Element[flist, i] > error, i, 1, 5) → toobig
  6. Segment(A, B) → f_1
  7. Sequence(Segment[(-2 + i, -0.12), (-2 + i, 0.12)], i, 0, 4, 1) → list1
  8. Sequence(Text[-2 + i, (x(C) + (1.02 * i), y(C))], i, 0, 4) → list2
  9. Sequence(Segment[(-2 + i, -0.11), (-2 + i, 0.11)], i, 0, 4, 0.5) → list3
  10. Sequence(Segment[(-2 + i, -0.09), (-2 + i, 0.09)], i, 0, 4, 0.25) → list4
  11. Sequence(Segment[(-2 + i, -0.07), (-2 + i, 0.07)], i, 0, 4, 0.125) → list5
  12. Sequence(sqrt(Random[1, 100]), i, 1, 5) → list9
  13. Sequence(RandomElement[{Element[list7_1, i], Element[list9, i]}], i, 1, 5) → list7_2