## 8.17.2011

### Basic axioms of mathematics

Mathematics is laws there is the surrounding world on that. The laws of mathematics are identical for any universes with any amount of measuring.

Mathematics - it governed without exceptions. If an exception appears in a mathematical rule - this rule must be changed. This statement is the universal formula of the scientific discovery in mathematics.

Mathematics is abstraction. The abstract of mathematics consists in that the laws of mathematics operate always and everywhere identically.

Mathematics is the closed system. If a correct mathematical result is got, then there is an infinite amount of ways resulting in an exactly such result.

Mathematics is symmetry. Absolute symmetry in mathematics is a limit of development of mathematics as sciences.

Mathematics is relativity. Positive and negative numbers do not exist in the wild. Positive and negative numbers are this reflection of our personal opinion in mathematics. A negative number is a sign of the relative system of coordinates, position of that depends exceptionally on our choice of her center. A the same point can have different signs and different numerical values in the different relative systems of coordinates.

Mathematics is basis of commonunication and mutual understanding of reasonable creatures from different civilizations. Geometry translators does not need. Mathematics is closed wherein human logic begins.

Expl for blondes: in more detail we will consider each of these axioms a bit later, and while we will continue an acquaintance with mathematics and will look at some concepts that will be used in future.

1. ...horror) Define, would you be so kind, for me is a word "axiom". Can you show laws out of these "axioms", about that talk in the nearby "opening"?)
I will be heavy to take apart all of it on constituents, but we will begin with the first "axiom".
How do you think - if geometry does not need explanations - what geometry you talk about: about Euclidean or not Euclidean? I talk about of Hyperbolic geometry. Yes, exactly about absence of fifth postulate. Honour at leisure, I will with impatience wait an answer, later to tell harsh truth.

2. I talk about geometry in a singular. And we examine her in Euclidean space or in space of hyperbolic geometry, depends on concrete terms. By the way, as I suppose, in hyperbolic geometry a fifth postulate nobody abolished. Naturally, we can on this occasion think whatever.

3. sabbat8310, then what you read is yet not horror. Horror I write down below on your own.

1. Euclidean and non-Euclidean geometries are concepts relative. What geometry will you describe the area of the room located on the surface of planet in?

2. Where is a border, separating Euclidean geometry from all other varieties of geometries? This border is determined by the degree of curvature that it is possible to ignore. In different cases a degree of neglect can be different, what determines relativity of concepts "Euclidean" and "non-Euclidean" to geometry.

3. Transition from Euclidean geometry to non-Euclidean geometry and back for all geometrical figures must be synonymous. Displacing and opening out Euclidean spaces over must not bring to distortions of geometrical figure.

4. Geometry is a trigger mechanism of gravitational collapse.