dots math sequence tends limit ie math display inline lim n infty n math exists said '''convergent''' otherwise '' 'divergent''' ''see section limits convergence details'' real valued sequence math n math '''''bounded''''' exists math r math math n math math n mathbb n math real valued sequence math n math '''''monotonically increasing''''' '''' 'decreasing''''' math display block leq leq leq cdots math math display block geq geq geq cdots math holds respectively either holds sequence said '''''monotonic''''' monotonicity '''' 'strict'''''
Formal science Mathematics Pure mathematics Analysis Real analysis