Comment on Banach–Tarski ParadoxparentComments−constantcrying2yWhy didn't you list the actual "standard" approach of accepting that certain sets have no definable volume? This is the basis of measure theory, which is perfectly accepting of the fact that measures don't need to be defined everywhere.−IngoBlechschmid2ySorry, I was in a hurry before, the standard approach is exactly what I wanted to refer to with option 1!
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Why didn't you list the actual "standard" approach of accepting that certain sets have no definable volume? This is the basis of measure theory, which is perfectly accepting of the fact that measures don't need to be defined everywhere.
Sorry, I was in a hurry before, the standard approach is exactly what I wanted to refer to with option 1!