## prerequisite

Basic definitions of fraction is a prerequisite here. This concept can be covered at a Kindergarten level. We are not requiring any fraction arithmetic yet. The terms "numerator" and "denominator" can be a mouthful, so we opt for "tops" and "bottoms" instead. This adds more context to the term "improper fractions" (now called "top heavy") and "proper fractions" (now called "bottom heavy").

### nouns

simple nouns are numbers and variables.

variables: are "blank numbers", or containers for amounts such as your age or test score. Variables are written as letters or shapes, such as

{\begin{aligned}x&={\textrm {Heather's\ age}}\\\heartsuit &={\textrm {Chandler's\ age\ }}=x+3\\\square &={\textrm {Chandler's\ testscore}}\end{aligned}}

compound nouns, aka layers, are combinations of verbs and nouns, and they are usually written with parentheses or shapes. Examples of nouns (simple and compound) are: 1, x, $\heartsuit$ , x + 1, y * ( x + 1 ).

anti-nouns are negative, reciprocal, log, and root

phrases are mathematical expressions. We prefer this term for syllabic brevity.

forward-nouns are positive numbers, integers (not reciprocals), and leaves

### verbs

verbs are operations like +, -, *, /, ^, 0--, --0, cos(), etc.

anti-verbs are minus, divide, log() and root(,)

forward-verbs are plus, times, powers

seed & repeater verbs: in the context of self-plus and self-times, the primitive operation is called the seed verb and the resulting operation from the repetition is the repeater verb. For instance, in 3x = x + x + x, the seed verb is "+" and the repeater verb is times. Likewise, x^3 = x * x * x has the seed verb "*" and repeater verb as "^".

The table below shows that most arithmetic traces back to the + verb.

 symbol verb common names example − anti-plus minus, subtract 5 − 3 = 2 * self-plus times, multiply 5 * 3 = 15 / santi-plus, short for "self-anti" divide 15 / 3 = 5 ^ self-times, or self-self-plus power, exponential 5 ^ 3 = 125the symbol ^ is only seen in computer programs. In math, this is written as 53 = 125 $\circ \!{\frac {\quad }{\quad }}$ left-divide, or anti-self-self-plus left (no acronyms :-) logarithm $\circ \!{\frac {125}{5}}=3$ ${\frac {\quad }{\quad }}\!\circ$ right-divide, or anti-self-self-plus right root ${\frac {125}{3}}\!\circ =5$ The Blead section of this book explains these verbs in detail.