Loading [Contrib]/a11y/accessibility-menu.js

• Discussion Results: what is a number?
  • Something about group theory
    • This is more like a way of telling us how to use numbers, not really a good definition.
    • Set up bounds to define things
  • Different classes (natural, real, imaginary)
  • Where do you draw the boundaries between objects?
  • A way to quantify the nature of living and reality
• Number Systems
  • We want them to be desirable and group-like
  • Types
    • Natural Numbers
      • Integers greater than zero
    • Whole Numbers
      • Natural Numbers + 0
      • 0 is the hole.
    • Integers
      • { …, -2, -1, 0, 1, 2, … }
      • Good for algebra, we'll see later
    • Rationals
      • Like \(\frac{1}{2}\).
      • A ratio/fraction/quotient of integers
    • Real
      • Like \(\pi\)
      • A number on the number line
        • A number that can be a distance to something.
        • A good enough definition that isn't "real analysis"
    • Complex Numbers
      • Like \(5i\)
      • There will be many complex numbers
        • Matrices with complex numbers can be different from real numbers
      • Complex plane
    • Hamaltonian numbers music video? #curiosity
  • Why do we want more numbers?
    • Why Zero?
      • Additive identity
        • Zero vector = identity vector
        • Frame of reference, starting point, nice and neutral
    • Zintegers?
      • Why negatives?
        • So you can make zero
        • Undo each other, undo a \(+5\)
        • Inverse
          • \(-a\) and \(a\) are additive inverses
  • That's all we need to get to a group: KBe2020math530refGroups

---