Numerical sequences

Order relationship of the reals, upper bound, density of rationals and irrationals.
Definition of sequences, operations (+, x, .), structure, real sequences increased, decreased, bounded, monotone.
Asymptotic behavior, quantified definition of the limit, uniqueness, all convergent sequences are bounded, operations on limits, links between limits and inequalities (Gendarmes theorem...)
Extracted sequences, monotone and adjacent real sequences, double linear recurrent sequences.., recurrent sequences with study plan (autonomy on f increasing, f decreasing in exercises)