Integers

Negative Numbers as Debt

Debt is put down in terms of a positive number but it has a negative connotation.

Total Wealth

The idea of an integer as representing total wealth, factoring in cash and debt. (cash is stand-in for assets because the word assets is a little bit foreign for many)

Reduction to one of them being zero and taking that for the symbol, using a negative sign if it is the debt that is positive.

Zero as cash equals debt.

Note different pairs that are equivalent represent different actual situations, but we ignore those equivalences.

Addition of Integers

Subtraction of Integers

Flip and add.

Multiplication of Integers

what it represents: one is amount of cash/debt; the other is representing repeated adding that amount or removing the amount. Removal of debt is adding cash.

Glimpse of Properties

commutative, distributive

Lines

For those familiar with lines (first chapter of next book), integers can be represented as lines with slope 1 with the integer being the place where the line crosses the x-axis. So y = x - i where i is the integer.

Representation of arithmetic on line. Reference line is y = x; use horizontal line segments from y=x to point in question, then do the operations.

sub 1

sub 2

sub 3

sub 4

sub 5

sub 6

sub 7