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I am wondering, from a formalized mathematical standpoint, if it makes sense to say A and B if B is a subset of A.

For example, machine learning and AI is a common expression in the software industry. AI here refers specifically to Deep Learning (in contrast to classical machine learning approaches).

But it is well-established that deep learning is a subset of machine learning, which is in turn a subset of the over-arching field of AI.

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...which would suggest that it does not makes sense to use the word "and" to compare Machine Learning to AI. In other words, the word "and" suggests machine learning and AI (deep learning) are different things, but they are not, as Deep Learning is a subset of Machine Learning, which is a subset of AI.

Asaf Karagila
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Cybernetic
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  • I love oranges and fruits. I say oranges to give you a specific example of a fruit I like. – Some Guy Mar 26 '21 at 18:49
  • Oh I see, from a formal mathematical standpoint, it doesn't matter, it is redundant, but it is not wrong – Some Guy Mar 26 '21 at 18:50
  • "Oranges and fruits" is nonsensical. – Cybernetic Mar 26 '21 at 18:50
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    @Cybernetic No, it's not nonsensical, it's just redundant and silly. – Noah Schweber Mar 26 '21 at 18:50
  • I don't have to mention oranges cause I said fruits, but I gave oranges as an example – Some Guy Mar 26 '21 at 18:51
  • "like" and "and" are not the same connector. – Cybernetic Mar 26 '21 at 18:52
  • Is "and" ever okay. I presume you mean the union and then $A$ "and" $B$ = $A\cup B$ which is equal to $A$. If $B$ "and" $C$ is ever correct (which I don't think it ever is) then I see nothing wrong with $A$ and $B$ meaning $A$. – fleablood Mar 26 '21 at 18:53
  • Oh.... or does "and" mean intersection? What does "mammals and carnivores" mean? If it has a mean applying the same meaning to "carnivores and lions" ought to logically be fine. "redundant and silly" but fine. – fleablood Mar 26 '21 at 18:56
  • Now you're not even using the connector "and". The whole point is whether the use of the connector "and" maps to the mathematical definition of sets and subsets, and if so, is it being used correctly when comparing sets and subsets in the English language. – Cybernetic Mar 26 '21 at 19:06
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    This is not a mathematical question. And natural language is not a formal language. I’ve voted to close. – symplectomorphic Mar 26 '21 at 19:07

1 Answers1

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No, in mathematics it is not an accepted idea. If you say $A$ AND $B$ the intersection is expected (provided the intersection make sense).

Davide Trono
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    If I say I have "oranges and lemons" then you might reasonably assume I have some oranges and I have some lemons, not just the empty intersection between them. – Henry Mar 26 '21 at 18:53
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    One thing is language, one thing is mathematics. Set theory is not semantics unfortunately (or luckly?). – Davide Trono Mar 26 '21 at 18:54
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    Little of this thread makes any sense, because people are talking about words and phrases out of context. Here for example: "If $A=L^1$ and $B=L^2$ then $A$ and $B$ are Banach spaces". A perfectly acceptable sentence using "A and B" that has nothing to do with $A\cap B$. – David C. Ullrich Mar 26 '21 at 19:23
  • good point, that is completely true. – Davide Trono Mar 26 '21 at 20:10