In a manner based on random choice or personal whim, rather than any reason or system. The tasks were assigned arbitrarily, without considering anyone's preferences or skills.
Without restraint, law, or accountability; based solely on individual will or authority. The ruler could confiscate property arbitrarily, ignoring established laws.
To any unspecified or required degree (typically used with words such as "small" or "large" in technical or mathematical contexts). Let ε be chosen arbitrarily small so that the limit exists.