what does arbitrary mean

The word “arbitrary” is an adjective that generally describes something chosen or decided without a clear reason, rule, or fair system —often just on whim, personal preference, or convenience.

Core meaning

In everyday use, “arbitrary” means:

• Not based on reason or evidence.
• Seemingly random or coming by chance.
• Made according to someone’s personal will, not an objective rule.

For example:

• An arbitrary decision is one that feels unexplained or unfair.

• An arbitrary rule at work might be one nobody can really justify with logic.

Common nuance: unfair or one‑sided

Beyond “random,” arbitrary often carries a slightly negative tone when power is involved:

• Unfair use of authority.
  A judge or boss acting arbitrarily is using power without clear rules or standards , which can seem oppressive or unjust.

• Capricious or unpredictable.
  People might complain if punishments or policies seem arbitrary because they don’t follow a consistent pattern.

Quick examples

• “The teacher graded the essays in an arbitrary way—students with similar answers got very different scores.” (feels random and unfair)

• “The new deadlines seem arbitrary ; no one has explained why those dates were picked.” (chosen on convenience, not a solid reason)

In math / logic

In more formal contexts, like math, “arbitrary” can mean any value you like, with no special restrictions , as long as it fits the general type.

For instance:

• “Let xxx be an arbitrary real number.”
  This means xxx stands for any real number, and the argument should work no matter which one you pick.

TL;DR:
“Arbitrary” usually means chosen without a clear reason, rule, or fairness , often with a hint that it feels random, biased, or unfair. In formal logic or math, it can mean “any value at all (with no extra restrictions).”