ფაილების კატალოგი

Simple and genius discovery.This is a conection between number theory and probability theory. A new door opened in probability theory.
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Let Q'(∧,∨)={m/n | 0≤m≤n, m,n are integers}, where ∧ and ∨ are operations.
Let a≤b and c≤d, then a/b∈Q' and c/d∈Q' and
a/b∧c/d=ac/bd∈Q' and a/b∨c/d=a/b+c/d-ac/bd∈Q'.
P r o v e
b-a≥0, c≤d, 
c(b-a)≤d(b-a),
cb-ca≤db-da,
ad+cb-ac≤db,
(ad+cb-ac)/db≤1,
a/b+c/d-ac/bd≤1.
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Let P(A) is probability and Q'(∧,∨)={P(A}, 
P(A)=P(B)P(Q)∨P(R), 0≤P(R)≤P(B),
P(A)≡P(R) (modP(B)).