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The next 3 videos build up the concept of Order structure of the real numbers. To understand the order properties we will first define the set of positive numbers and use it to prove the further properties.
In the first video we will look at the axioms related to the set of positive numbers and then prove the Trichotomy law of real numbers.
In the second video we will try to relate the algebraic properties of R to the order properties. Finally, in the last video explains the consequence of these properties, we will explain why 1>0 and that all natural numbers are greater than n.
Order properties of R
Order properties compatibility
Consequence of algebra and order structure
