77. Irrational numbers (continued)
Full lesson: http://childrenscience.ru/courses/sav...
In this lesson, we prove a theorem on the density of the set of linear combinations of integers and irrational numbers on the number line, and also construct an extension of the ring of integers and the field of rational numbers by adding an irrational number.
00:00 Density Theorem
06:10 Looping a Line
09:09 Completing the Proof of the Density Theorem
17:22 Ring ℤ[𝛼] and Field ℚ(𝛼)
22:48 Structure of ℤ[𝛼]
29:08 Structure of ℚ(𝛼)
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