One day, a vector space was involved in a hit-and-run in a carpark and, while not fatally injured, was sent to the hospital for surgery. Due to its poor healthcare plan, a bill of thousands was incurred. The vector space was not by any means in poverty, but thousands is a lot for anyone to pay out of pocket, and so it decided to try to track down whomever had hit it.
After returning to the carpark and reviewing the security camera footage with the police, it was discovered that the one who hit the vector space was none other than the axiom of choice itself. Now, it just so happened that the axiom of choice was one of the vector space's employees, and was notorious for not showing up to events on time — if at all. The vector space decided to speak to its lawyers, and soon a court date was arranged — the 12th of September, 10am sharp.
On the day of the court appearance, the vector space and its lawyer showed up to the courthouse early and waited patiently for all involved parties to show up. One by one, people started filling up the benches in the courtroom, but someone was conspicuously missing — the defendant itself, the axiom of choice. As the clock slowly ticked up to 10am, the vector space grew more and more restless: why wasn't it showing up? Where could it be? What did this mean for its case?
10am quickly turned into 10:15am, and then 10:30am, and by 11 the axiom of choice had still not made an appearance. At this point, the vector space's lawyer motioned for a recess. As people started leaving the room, the vector space turned to its lawyer with a puzzled look and said, "What's going on? If the defendant doesn't show up, does that mean I automatically win the case?"
The lawyer responded, "I'm sorry, but without the axiom of choice, you might not have a basis."
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