unbounded(s = adj.all) boundless, limitless - seemingly boundless in amount, number, degree, or especially extent; "unbounded enthusiasm"; "children with boundless energy"; "a limitless supply of money"
Derived form noun unboundedness₁

   Having no bound or limit; as, unbounded space; an, unbounded ambition. [1913 Webster]

unbounded, adj. not bounded; infinite (unbounded optimism).

Derivative:
unboundedly adv. unboundedness n.

N  infinity, infinitude, infiniteness, perpetuity, boundlessness, infinite, immense, numberless, countless, sumless, measureless, innumerable, immeasurable, incalculable, illimitable, inexhaustible, interminable, unfathomable, unapproachable, exhaustless, indefinite, without number, without measure, without limit, without end, incomprehensible, limitless, endless, boundless, termless, untold, unnumbered, unmeasured, unbounded, unlimited, illimited, perpetual, infinitely, ad infinitum, as boundless as the sea.

unbounded interval