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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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
9th-10th Foundation

Foundation of Algebra with Numerical Arithmetics

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`.

(click for the list of pages in the lesson)