Operations and Functions

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n mathematics ... just what constitutes an operation or function? An operation is the "action" of mathematics while the operand (constant, variable, etc.) is the "thing" or object acted on. The correspondence with physical reality is absolute. What you are daily looking at is the concretization of mathematical-logical principles. Hence, there is at base only one operation ... it is addition (and its concomittant ... subtraction).

There are several other manmade operation sets which are composed of commonly used arrangements of the primary operation.

Multiplication is such a set and consists of "multiple additions" carried out in one "operation", vis. 6x7=42 means add one + one ... to get six, then add one set of six to another, to another ... seven times to get the 42.

One advantage of multiplication is that as well as multiple additions, the numbers 6 and 7 are "married" to each other, i.e. they become "functions" of one another in the process of creating the concept of 42.

Of course, to the universe of inanimate matter such marriages are meaningless. A more lucid example is the divisional marriage of length to time to get velocity. Such conventions assist us in predicting the outcome of events in an ordered world.

The concepts we form are ultimately based on the absolute foundation of simple addition (the only true, independent operation). For instance, we have the string 0010101010100100001010111010101111100 and make observations about cardinality and ordinality.

To consider cardinality we may take it as a base two number and translate it into base ten for everyday use or we might take the 0's as simple placetakers denoting separation in time or space along a number line ... while relative ordinality can only be considered by connecting the two ends in a two-dimensional closed loop.

Relative ordinality is the relation of one thing to another while determinate ordinality is the relationship of a thing to another by way of its relationship to an absolute reference ... in the case of the number line, the "0" point.
Such things are the "stuff" of existence from which all else is built. Thus, a dog is a logical-mathematical construct when completely done in by reductionism.

So there is but one fundamental operation (addition). Then several others which are in fact elementary "functions". And hoards of actual "functions" which are "operation sets" which human beings have found useful and are therefore assigned there own name (symbol).

There is now, just in the 20th century, the development and implementation of the next higher level.

Operation - Function - Program

A program is simply a set of sets of the elementary operations. It was not developed till now because the human mind is incapable of utilizing such large quantities of mathematical information at once. Prior to the computer, the closest thing to a "program" was a lengthy book proof of a mathematical proposition.

Is this difficult to understand?
Yes, initially ...



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