There are several other manmade 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
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
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 Such things are the "stuff" of existence from which all else is built. Thus, a dog is a logical-mathematical construct when completely by reductionism.
done inSo 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 - ProgramA 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 lengthybook proof of a mathematical proposition.
Yes, initially ... |