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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Welcome to the *revolutionary and ingenious* formal foundation of algebra with Numerical Arithmetics.

Algebra is based on the following basics of numerical arithmetics.

• PEMA Precedence Order (Parenthesis, Exponent, Multiplication, and Addition)

Subtraction is inverse of Addition

Division is inverse of Multiplication

Root and Logarithm are two inverses of Exponent

• CADI Properties of Addition and Multiplication (Closure, Commutative, Associative, Distributive, Identity, Inverse).

• Numerical Expressions are statement of a value

• Value of a Numerical Expression does not change when modified per PEMA / CADI

• Equations are statements of equality of two expressions

• And statement of equality does not change ...(explained in the lesson)

• And so for In-equations *(click for the list of lessons in this topic)*

Numerical Arithmetics: Laws and Properties for Algebra

Formal foundation in Algebra is established with laws and properties of Numerical Arithmetics.

• Comparison : Trichotomy and transitivity properties.

• Addition : Closure, commutative, Associative, Additive Identity, Additive Inverse properties

• Subtraction : Handled as inverse of addition, and holds properties of addition. eg: Commutative property `a-b = a+(-b) = -b+a (!=b-a)`

• Multiplication : Closure, commutative, Associative, Distributive over addition, Multiplicative Identity, Multiplicative Inverse properties

• Division : Handled as inverse of multiplication, and holds properties of multiplication. eg: `a-:b(c+d) ``= a xx (1/b)xx(c+d) ``= axx (c/b + d/b)` `!= a-:(bc+bd)`

• Exponents : Addition, multiplication, division properties of exponents.

The above is *exemplary and ingenious foundation* in learning algebra. For example, `x+(y+x)` is simplified using the commutative law `= x+(x+y)` and the associative law `= 2x+y`.