the.com/axioms
the rules you don't get to argue with, only build on.
means statements accepted as true without proof, used as the starting foundation for a logical or mathematical system.
from from greek axioma, meaning that which is thought worthy or fitting, from axios, worthy — euclid used them around 300 bce as the self-evident starting points for geometry.
euclid's fifththe parallel postulate took 2000 years to question
godel's blowany system rich enough can't prove its own axioms consistent
choice controversialaxiom of choice lets you pick from infinite sets, still debated
not truthsaxioms are assumed, never actually proven correct
for instance
euclid's postulates — five rules built all of classical geometry, 300 bce
zermelo-fraenkel axioms — nine rules underpinning nearly all of modern set theory
peano axioms — 1889 rules defining the natural numbers from scratch
non-euclidean geometry — dropping one axiom in 1830 created entirely new universes of math