What is Numerical Equivalence of Sets and How is it Defined?

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Numerical equivalence of sets is defined as the existence of a bijective function between two sets, indicating they have the same cardinality. Some participants express uncertainty about the depth of this definition and whether it requires two injective functions or just one bijective function. The term "numerical equivalence" is less commonly used compared to "same cardinality." The consensus leans towards the sufficiency of a single bijective function for establishing equivalence. Overall, the discussion clarifies the concept of numerical equivalence in the context of set theory.
Piglet1024
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1. Define numerical equivalence of sets
2. I'm not sure how in depth the definition needs to be, how is my current def?
3. X is numerically equivalent to Y if \existsF:X\rightarrowY that is bijective or there are two injective functions f:X\rightarrowY and g:Y\rightarrowX
 
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Seems reasonable. I haven't seen the term "numerical equivalence" used. What I have seen is "same cardinality." I don't think you need to have two injective functions; just one bijective function should do the job.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
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