Editing 804: Pumpkin Carving
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The off-screen interviewer in that frame references the {{w|Axiom of Choice}}. This axiom is the foundation for many theorems (including the Banach–Tarski paradox) and is extremely influential to modern mathematics; however, it has been historically controversial precisely because it enables this kind of weirdness. It is called an "axiom" because it is a statement that is not meant to be proven or disproven—only accepted or rejected depending on the theoretical framework one wishes to work with. Rejecting the Axiom of Choice results in a perfectly coherent alternate form of set theory. Since the proof for the Banach–Tarski paradox relies on accepting the axiom of choice, the interviewer is suggesting Cueball's unexpected result would not have happened without using the axiom. | The off-screen interviewer in that frame references the {{w|Axiom of Choice}}. This axiom is the foundation for many theorems (including the Banach–Tarski paradox) and is extremely influential to modern mathematics; however, it has been historically controversial precisely because it enables this kind of weirdness. It is called an "axiom" because it is a statement that is not meant to be proven or disproven—only accepted or rejected depending on the theoretical framework one wishes to work with. Rejecting the Axiom of Choice results in a perfectly coherent alternate form of set theory. Since the proof for the Banach–Tarski paradox relies on accepting the axiom of choice, the interviewer is suggesting Cueball's unexpected result would not have happened without using the axiom. | ||
| − | The title text references a biblical story involving {{w|Solomon|King Solomon}}. In the story, known as the {{w|Judgment of Solomon}}, two women were brought before him both claiming that a particular child was their own. Solomon tested the women by saying the only solution was to cut the baby in half and give each woman one of the halves, knowing the real mother would fight to save her child's life even if the price was giving up the whole child to the other woman. The joke is that if Solomon had developed the Banach–Tarski theorem first, then he could have actually believed cutting the baby into pieces was a valid solution. In that scenario, he would have tried to make two whole children from the original and given one to each woman. However, since babies are not infinitely divisible,{{Citation needed}} his attempt would have failed miserably and set back set theory for centuries due to the appearance that he has "proved" the theorem wrong. Note that the title text actually mentions ''attempts'' indicating that King Solomon killed several babies in this fashion. | + | The title text references a biblical story involving {{w|Solomon|King Solomon}}. In the story, known as the {{w|Judgment of Solomon}}, two women were brought before him both claiming that a particular child was their own. Solomon tested the women by saying the only solution was to cut the baby in half and give each woman one of the halves, knowing only the real mother would fight to save her child's life even if the price was giving up the whole child to the other woman. The joke is that if Solomon had developed the Banach–Tarski theorem first, then he could have actually believed cutting the baby into pieces was a valid solution. In that scenario, he would have tried to make two whole children from the original and given one to each woman. However, since babies are not infinitely divisible,{{Citation needed}} his attempt would have failed miserably and set back set theory for centuries due to the appearance that he has "proved" the theorem wrong. Note that the title text actually mentions ''attempts'' indicating that King Solomon killed several babies in this fashion. |
The axiom of choice and set theory was later referenced in [[982: Set Theory]] and, much later, the axiom of choice was mentioned again in the title text of [[1724: Proofs]]. | The axiom of choice and set theory was later referenced in [[982: Set Theory]] and, much later, the axiom of choice was mentioned again in the title text of [[1724: Proofs]]. | ||
