What is the difference between hint and imply?
I'm curious, could you explain the distinction between the words "hint" and "imply"? It seems to me that they are often used interchangeably, but I have a feeling there's a subtle nuance between the two that I'm missing. When someone hints at something, are they being more direct than when they imply it? Or is it the other way around? I'd appreciate your insights on this linguistic question.
Does apx hard imply NP hard?
Could you please clarify for me the relationship between "APX-hard" and "NP-hard" in the context of computational complexity? Specifically, I'm wondering if a problem being APX-hard necessarily implies that it is also NP-hard. Could you elaborate on the implications and potential differences between these two classifications, and provide any examples to further illustrate your points?
Does abelian imply normal?
Excuse me, but I've been pondering over this mathematical concept and I'm a bit confused. Can you clarify for me if the term "abelian" inherently implies that a group is also "normal"? It seems like there might be some overlap in properties, but I'm not entirely sure. Could you please explain the relationship, if any, between these two concepts in simple terms? Thank you for your time and assistance.