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There are multiple interpretations to the question, clearly. Removing a tick mark from an infinite number line would just cause all the other tick marks to sli
by pavement 9y ago
There are multiple interpretations to the question, clearly.
Removing a tick mark from an infinite number line would just cause all the other tick marks to slide closer together like billiard balls, no?
Or is the question really about what happens if we render six as a forbidden, unaddressable element? Maybe equations normally resulting in an integral six, or involving an integral six return an error stating: undefined? Not unlike a divide by zero error?
Consider rationalizing division by zero. One could interpret the outcome of such an operation as always resulting in zero, instead of an error, but what would that mean when modeling real world events? If you have zero, and you want to divide it into N number of parts, well, you’d still have zero things, and so what? But what if you had somethings, and you wanted to divide them all into zero parts? Does that mean the operation represents the total annihilation of those things?
We can imagine a situation where total annihiliation by division is possible, but is it worth building that interpretation into most models, when an operation like that isn’t often applied to circumstances, and such an outcome is rarely requested?
- derefr 9y agoMy understanding is that the math professor interpreted the question to mean "what if our universe, rather than acting in so-far-seeming correspondence with ZFC set theory, was one that was best explained by a different axiomatic set theory—one that didn't entail the existence of "6" as a mathematical object? What universe would we be in, and what would it be like?"