@utabintarbo: I didn't decide your understanding of axioms was inadequate when you disagreed with me; I decided that when you made wrong statements. I can also quote things:
Quote:
From Wikipedia:
An axiom is any starting assumption from which other statements are logically derived. It can be a sentence, a proposition, a statement or a rule that forms the basis of a formal system. Unlike theorems, axioms cannot be derived by principles of deduction nor demonstrable by formal proofs—simply because they are starting assumptions—there is nothing else they logically follow from (otherwise they would be called theorems). In many contexts, "axiom," "postulate," and "assumption" are used interchangeably.
As seen from definition, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results. To axiomatize a system of knowledge is to show that some of its claims can be derived from a small, well-understood set of sentences. This does not imply that they could have been known independently; and there are typically multiple ways to axiomatize a given system of knowledge (such as arithmetic). Mathematics distinguishes two types of axioms: logical axioms and non-logical axioms.
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P.S. It would be nice if you would include citations when you quote things.
For the record: Euclid was not wrong. He was correct in the plane. It was later discovered that there are alternate geometries, not that his was wrong. In fact, much geometry is still based on his work.