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Definition of unbounded : Having no bound or limit; as, unbounded space; an, unbounded ambition.

Synonyms:

crashing, out-and-out, flat, positive, complete, limited, perfect, arrant, all-out, unmitigated, damned, consummate, unfathomable, pure, unqualified, unrelieved, dead, plain, absolute, downright, measureless, thorough, sheer, thoroughgoing, total, flat-out, unequivocal, big, utter, unreserved, unmeasured, blooming, outright, loose, unconditioned

immemorial, unlimited, interminable, inexhaustible, perpetual, eternal, bottomless, infinite, everlasting, boundless, innumerable, countless, illimitable, ceaseless, numberless, termless, timeless, endless, limitless, incalculable, immeasurable

Usage examples:

• Her faith was unbounded. - "The Son of his Father", Ridgwell Cullum.
• A most useful man in the field was the honest carrier, whether at point or at any other place where the ball comes sharp and quick; for, to quote Shakespeare, " he was a man Of an unbounded stomach." - "A Cotswold Village", J. Arthur Gibbs.
• He carried with him the unbounded love and devotion of one of the finest armies that ever the world had seen; and the attachment, hardly less energetic, of all those classes of society throughout Italy, who flattered themselves with the hope that the Cisalpine Republic, the creature of his hands, would in time prepare the way for, and ultimately merge in a republican constitution common to the whole Italian people. - "The History of Napoleon Buonaparte", John Gibson Lockhart.