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Similarity is

- reflexive: x is similar to x
- symmetric: if x is similar to y then y is similar to x.
- transitive: if x is similar to y and y is similar to z then x is similar to z.

Q: What are the axioms of similarity?

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They are called axioms, not surprisingly!

Axioms cannot be proved.

Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.

No. Axioms and postulates are statements that we accept as true without proof.

No, not at all. The Incompleteness Theorem is more like, that there will always be things that can't be proven. Further, it is impossible to find a complete and consistent set of axioms, meaning you can find an incomplete set of axioms, or an inconsistent set of axioms, but not both a complete and consistent set.

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Peano axioms was created in 1889.

Axioms - album - was created in 1999.

They are called axioms, not surprisingly!

Axioms cannot be proved.

axioms

Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.

No. Axioms and postulates are statements that we accept as true without proof.

An Axiom is a mathematical statement that is assumed to be true. There are five basic axioms of algebra. The axioms are the reflexive axiom, symmetric axiom, transitive axiom, additive axiom and multiplicative axiom.

No, not at all. The Incompleteness Theorem is more like, that there will always be things that can't be proven. Further, it is impossible to find a complete and consistent set of axioms, meaning you can find an incomplete set of axioms, or an inconsistent set of axioms, but not both a complete and consistent set.

axiomas is the Spanish word that is translated into English as axioms. Axioms are concepts that are accepted as true without proof.

The cast of Axioms of a Dishwasher - 2010 includes: Zach Bainter as Dishwasher

Your question is somewhat hard to follow, but it is a fact of logic and mathematics that if the set of axioms are inconsistent, then every statement in the language of the axioms can be proven. (You can always get a proof by contradiction just from axioms along )