Math phylosophy that we are counting objects of th

Math phylosophy that we are counting objects of the same type.
Math phylosophy that we are counting objects of the same type.
A number 1 represents a single object.
A number higher than one represents a group of similar objects.
Addition = creating a group of two groups objects.
Substraction = creating a group with part of the objects of one other.
Multiplication = creating a group consisting of a given number of similar size groups.
Division = creating a number of similar size groups from one group



All the math ops are performed by addition. We create a new group and
add numbers to the new group. Numbers from other group (subtraction) etc~.
Fractions.
Fractions does not exist. A fraction has other units and we count fractions as integers.
Half apples are counted seperately from the full apples and at the end are marked with
the right units.
The classic fractions have a phylosophical problem : multiplication which leads to
less than the original value.

The solution is that there can not be a group of objects with half object :
the objects have to be the same type. Therefore in case of fractions they have to be multiplied
by a scalar, then multiplied, and then divided by scalar.

The right solution is always to count fractions as integers. The last op can be to
transfer all the objects (singles and halves) to one units. A third group will be
with units of  1.5 apple. Its number is still integer. Fraction number is applied
only to units.

This phylosophy is applied in computers. All the ops are addition based. We add,
subtract, divide or multiply numbers by creating a new area in memory and
adding to the area a certaing number of numbers. The new area is our answer
to the calculation.