User:Numiri/KinderCalculus/nouns, verbs, adjectives

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, verbs, adjectives
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

$$ \begin{align} x         &= \textrm{Heather's\ age}\\ \heartsuit &= \textrm{Chandler's\ age\ } = x + 3\\ \square   &= \textrm{Chandler's\ test score} \end{align} $$

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. The Blead section of this book explains these verbs in detail.

adjectives adjectives are the negative & reciprocal noun modifier. They can be introduced as a reflection of a noun about the verb's center. (the center of a verb + or * is the group-theoretic identity 0 or 1 respectively)