MEMO 3.6

 

 

What is meant by the words ‘algebra’ and ‘algebraic’?  To the layman or non-mathematician, they mean that branch of mathematics which originated in Babylonia (around 1600 BCE) and in which one learns to calculate an unknown quantity with abstract variables and negative values instead of just the positive numbers of arithmetic.  (E.B., Vol. 1, p. 607)  The word ‘algebraic’ may also mean the substitution of symbols or letters for concepts in order to understand or express by mathematical formulas or equations more clearly and simply the relationships between such concepts.

On the other hand, with respect to the 19th and 20th century pure mathematician or scientist, the word ‘algebraic’ also means and involves the sophisticated theoretical study of abstract mathematical structures (such as fields, lattices, and vector spaces, etc.) that are constructed with complicated mathematical axioms (i.e. formal rules of operation and defined relationships) often in multiple theoretical dimensions.  (see Id., pp. 607 – 608)  This highly theoretical, abstract and axiomatic point of view continues to this day.

In any event, it is essential with all forms of algebra “that the calculations…involve only a finite number of quantities and end after a finite number of steps.”  (Id., p. 607)  Therefore, the concepts of ‘infinity’ and ‘eternity’ have no place in algebra.