Algebra (from Arabic: الجبر (al-jabr, meaning "reunion of broken parts" and "bonesetting") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
this is the wikipedia introduction about algebra. It looks that it’s the kingdom of the rules and the letters math nightmares.
In fact it’s clearly the world of equilibrium. As we where talking about this algorithm produced by the number line with a math teacher, he told me that géométry is an algebra while i was saying algebra is geometry.
It’s because algebra permit to generalize to more dimensions than geometric spaces. It took me few weeks to recall this dimension. And as math is art to generalize (Raymond Poincaré), we have in a certain sense have to translate the geometry of the number lines speech in algebraic language.
Yesterday, i have discover Alain de Connes. It’s the first time i heard a mathematician talking about the relationship between primes and space time. he was aiming to push his students in this ways for the research fundamental!
Awesome! So i take a look to one of his conference about mathematical language at the college the France. He was clearly trying to put them away from the academic views. He told about a book where intuitionism is clearly used. And show how sometimes some teachers make horrible mistakes when they put badly the questions.
It’s in this perspective that i want to place this revision of the vocabulary and the elementary rules.
Let’s speaks about equal sign.
When we manipulate numbers or quantities we perform what are commonly called operations.
if we generalize, there is a symbol which establishes the first equilibrium relation it is the equal sign. The equation equals equilibrium sign. like two objects that we compare in order to confuse a common identity. The balance shows us only one thing. Binary it answers us yes or no. In which case if it is not equal it is different. There is a primary articulation of reasoning, which is called logic.
This first relationship therefore basically involves two elements. As a result, it is necessary to specify the elements of which a dimension must be common. If they have a dimension in common, it is that they are the elements of the same set (distance from electric field ground what you want when they have).
There is an interval game because our two elements which surround the equal sign give birth to a third element of another nature: the relation.
For me it is as if 1 = 1 implies self-awareness. Because if 1 is equal to itself it knows that it is. It is identical to itself. Any form of intelligence can do this reasoning. It is even like the first thought towards self-awareness.
The earliest human number systems were unary. They counted their objects with stones. Many anthropologists explain that this system of account of the shepherd, was at the origin of the writing, and even of the seals. A hollow earth ball could contain closed objects, the number of which was written on the surface. These balls could then travel. The system improved with pottery, and the invention of an increasingly complex language.
As we are measuring animals, we have developed numerous measuring devices to punctually check the balance of a physical economic situation or what we want.
the algebraic reasoning which results from it is unstoppable: if x = y then y = x they are confused they overlap and therefore they are identical. In short, this is what equality tells us. And thereby all the formulas of algebra. We can say It is in my opinion a fundamental point and even a fundamental question, which is the big X?
Another notion that arises is unity in diversity. as soon as the balance is established, there are always several ways to say the same thing. the pythagorean theorem has no less than 370 demonstrations. There are endless ways to write 1. This is also why we need to practice. The next text will deal with fundamental operations.
now mystical links (by taping unary system i didn't look yet