11 ms·
Yea, the statement is missing "locally constant". It's a poor example given the assumptions are not clearly stated.
by bmitc 5y ago
Yea, the statement is missing "locally constant". It's a poor example given the assumptions are not clearly stated.
- pfortuny 5y agoOh, these kind of problems happen time and again in real-life maths: you use a lemma until someone points out that you are assuming something which may not take place (like connectedness of the domain, here).
- bmitc 5y agoYea, but like I said, it's a poor example as a "false belief" in this context, because as stated, it isn't false for some unwritten assumptions and is false for other unwritten assumptions. In mathematics, well and actually everything, the importance of assumptions is paramount. The problem is just ill-stated. This happens in engineering and software all the time. Time and time again, issues being resolved usually revolves around clarifying assumptions.