The phrase "an unbounded amount" is correct and usable in written English.
It can be used when referring to a quantity that is limitless or not restricted in any way.
Example: "In theoretical physics, we often discuss the concept of an unbounded amount of energy in the universe."
Alternatives: "an infinite amount" or "a limitless amount".
For starters, (i) a machine that requires an unbounded amount of matter running for an infinite amount of time will malfunction with probability 1, rendering it useless (Button, 2009, 779), and (ii) the huge, rotating black hole that is closest to us is probably out of our reach as well as our descendants' reach (see also Németi and Dávid 2006, Andréka, Németi, and Németi 2009).
The increased computational cost is twofold: increased memory requirements, since we need to store the history of the dominating process as well as the sequence of random numbers used to update the coupled chains; and longer running times, since we need to extend the process backwards for an indefinite (unbounded) amount of time.
To ensure these performance bounds, BSC requires a bounded variant of Eppstein's set reconciliation protocol that ensures that individual steps in the protocol cannot consume unbounded amounts of bandwidth.
With its resemblance to an unbounded corkboard, and its contributors' penchant for anonymity, Pastebin is hard to sum up.
He was a man of strong principles and integrity and had an unbounded capacity for empathy.
For a less gifted mind, such an unbounded menu of sound could so easily produce chaos.
For new-music partisans, at least, the development has been an unbounded cornucopia.
One painting of drunken revelry reveals that even then, writers on occasion had an unbounded thirst.
What we saw was merely the tiny tip of an unbounded peril of gigantic proportions.
A spider's — or a painter's — fleeting stab at perfection is a negligible stitch in an unbounded fabric.
He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite.
