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Yes, I do believe that those are the same things. I have a long-lasting history in math and when my students ask me this question, I am always positive that, in math, these two terms can mean the same thing in different instances. For example, if a number is not a real number, it can be undefined as well (and vice versa). If someone came up to me and asked me this exact question, I would say that the two terms mean the same thing.

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Q: Is undefined the same thing as not a real number?
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