>>12114937It's actually not that easy. But an interesting excercise.
You can start with a few statements about something. Something that's clearly bounded and defined. Consider what those statements are about. What do they talk about? What are the elementary objects they deal with? What are some i herent qualities of those objects?
For example, you can construct some axioms on basket weaving. Perhaps you want to know if you can arrange some patterns on the surface of a basket, or how wide it can get from a starting point, or if you can create some shapes (like adding handles) from a starting configuration.
You can start defining a straw, and some properties on it. A straw runs continuously without interruption. A straw is bounded on its length by two endpoints (or it could be not necessary to have this constraint, actually). A weave is a specific arrangement of straws around a closed geometrical figure (the base of tbe basket). You can start from a weave and perform simple operations on any two straws, they probably need to be adjacent for this. Any such operation results in a new weave.
There are some other rules. Straws cannot intersect. Either other straws or themselves. Straws do not form loops.
You start from there, through experimentation. Adding or removing basic assumptions as you find you need them.
It's in general not clear-cut. Euclid missed the continuity axiom which would be needed for his very first result. Of course, it was self-evident, so much that he didn't even thought of it needing to be stated. But of course that's just what an axiom is.
