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Order of Operation

- Parentheses
- Exponents and Logarithms
- Formal Function Notation:
**^(base, power)** = base ^ power = *number*
- exponent = index = power
*number* - what's the formal name?

- Formal Function Notation:
**log(base, ***number*) = log_base_ *number *= logarithm
- Underscores
* *represent subscript begin and subscript ends
*number* - what's the formal name?

- Multiplication AND Division

- Formal Function Notation: ⋅
**(multiplicand, multiplier)** = multiplicand ⋅ multiplier = multiplicandmultiplier = product

- Formally, (scalar) multiplication should be
*juxtaposition*, but that means 12 = 21 = 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.
- Note that cross product, ×, should be exclusively use for cross product, but it is a common mistake for scalar product in Arithmetic.
- The Cartesian Product is slightly larger than the cross product symbol, but people cannot distinguish them in written form.

- Formal Function Notation:
** /(dividend, divisor) **= dividend / divisor = quotient

- Note that obelus, ÷, should be use for ratio like it was traditionally used, not the modern division.
- 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.

- Addition AND Subtraction

- Formal Function Notation:
**+(addend, addend)** = addend + addend = sum

- commutative property is required

- Formal Function Notation:
**-(minuend, subtrahend)** = minuend - subtrahend = difference

- 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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