Question

Explain all the axioms of mathematics in 1 line

Answer 1

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Axioms:
(1) There exists at least 1 line.
(2) Every line has exactly 3 points on it.
(3) Not all points are on the same line.
(4) For each 2 distinct points, there exists exactly 1 line on both of them.
(5) Each two lines have at least 1 point on both of them.
a. Prove that for each two distinct lines, there exists exactly one point on both of them.
b. Prove that every point has exactly three lines on it.
c. How many points are in this geometry? Prove it!
d. How many lines are in this geometry? Prove it!
e. What does this geometry “look” like? Describe or draw a representation.
f. Explain which Axioms of Fano's Geometry are true statements in Euclidean Geometry.
g. Explain which Axioms of Fano's Geometry are false statements in Euclidean Geometry