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

On the other hand,
with respect to the 19^{th} and 20^{th} 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*.

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*.