Friday, August 12, 2016

Order of Operation

  1. Parentheses
  2. Exponents and Logarithms
    1. Formal Function Notation: ^(base, power) = base ^ power = number
      1. exponent = index = power
      2. number - what's the formal name?
    2. Formal Function Notation: log(base, number) = log_base_ number = logarithm
      1. Underscores represent subscript begin and subscript ends
      2. number - what's the formal name?
  3. Multiplication AND Division
    1. Formal Function Notation:  ⋅(multiplicand, multiplier) = multiplicand ⋅ multiplier = multiplicandmultiplier = product
      1. Formally, (scalar) multiplication should be juxtaposition, but that means 12 = 21 = 2.
      2. Note that dot product, ⋅, should be exclusively used for dot product, but is is common to use for scale product with numbers as noted: 12 = 21 = 2 would be problematic.
      3. Note that cross product, ×, should be exclusively use for cross product, but it is a common mistake for scalar product in Arithmetic. 
        1. The Cartesian Product is slightly larger than the cross product symbol, but people cannot distinguish them in written form.
    1. Formal Function Notation:  /(dividend, divisor) = dividend / divisor = quotient
      1. Note that obelus, ÷, should be use for ratio like it was traditionally used, not the modern division.
      2. In Algebra, Modulus (remainder function, not Complex Modulus, the Complex Magnitude function) uses the solidus, /, such as: Z/n. Alternatively mod is used, such as: A mod B = C.
  4. Addition AND Subtraction
    1. Formal Function Notation: +(addend, addend) = addend + addend = sum
      1. commutative property is required
    2. Formal Function Notation: -(minuend, subtrahend) = minuend - subtrahend = difference
  5. Ratio
Note that Ratio either modernly written with a colon, :, or traditionally with an obelus, ÷, has Last Order of Precedence as noted by Matthew Compher.

Division is either by solidus, /, or vinculum (a horizontal line where the numerator is above, and denominator is below).

The obelus is a line operator. Arguments before the obelus becomes the numerator and arguments after the obelus becomes the denominator as would be for Ratio, not Division.

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