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It's not so easy. I really was looking for those 2 (NN and ZZ) recently and had a fight. Also bijective function, problem is I can read about it all day but I n

It's not so easy. I really was looking for those 2 (NN and ZZ) recently and had a fight. Also bijective function, problem is I can read about it all day but I need an intuitive understanding (which I do have now but wasn't born with it). > about the domain and codomain I was taught these as domain and range. Another notational inconsistency. I basically agree with you but maths is a lot harder for some reason than programming. I don't think it's just me either. Perhaps if we could animate maths... I don't know. It's simply not an easy thing.

doubleunplussed 6y ago
Codomain and range are not the same - range is the set of numbers that actually come out, codomain is like, some kind of set that those numbers are drawn from like the integers (I'm not even sure, but it has never mattered enough for me to find out). For the case of a bijection of course the codomain and range are going to be the same, but not in general. But, there are ocassional renamings of things that usually improve the overall lingo. Some things I learned one way but they have now been renamed. E.g. I learned about 'one-to-one and onto' functions instead of 'bijective' functions. I think you'll agree 'bijective' is better than 'one-to-one and onto'. The same happens in programming languages and libraries when they rename functions from time-to-time. For a while there are inconsistencies whilst both are in use, sometimes permenently if the new name comes about by a creation of a new programming language or dialects. It's true that searching for a strange symbol you don't know the name of (or even have the unicode character - if it exists - on hand) is hard. If you knew they were called "blackboard-bold Z" you'd be able to find out via google what it meant pretty easily. (I am totally assuming you mean blackboard bold by writing ZZ and NN, otherwise I also don't know what those mean)
- throwaway_pdp09 6y ago
  "Codomain and range are not the same" - Umm. Interesting. Not aware of this. "I learned about 'one-to-one and onto' functions instead of 'bijective' functions" - For a beginner? The former. Past beginner? The latter. It's context. The "strange symbols" I only came across when searching for are described as double-struck. I only found that recently. I only found out yesterday they were also called Blackboard, while replying to others here. Difficulty in finding symbol meanings are no way the hard part of maths, though.

doubleunplussed 6y ago

Codomain and range are not the same - range is the set of numbers that actually come out, codomain is like, some kind of set that those numbers are drawn from like the integers (I'm not even sure, but it has never mattered enough for me to find out). For the case of a bijection of course the codomain and range are going to be the same, but not in general. But, there are ocassional renamings of things that usually improve the overall lingo. Some things I learned one way but they have now been renamed. E.g. I learned about 'one-to-one and onto' functions instead of 'bijective' functions. I think you'll agree 'bijective' is better than 'one-to-one and onto'. The same happens in programming languages and libraries when they rename functions from time-to-time. For a while there are inconsistencies whilst both are in use, sometimes permenently if the new name comes about by a creation of a new programming language or dialects. It's true that searching for a strange symbol you don't know the name of (or even have the unicode character - if it exists - on hand) is hard. If you knew they were called "blackboard-bold Z" you'd be able to find out via google what it meant pretty easily. (I am totally assuming you mean blackboard bold by writing ZZ and NN, otherwise I also don't know what those mean)

throwaway_pdp09 6y ago
"Codomain and range are not the same" - Umm. Interesting. Not aware of this. "I learned about 'one-to-one and onto' functions instead of 'bijective' functions" - For a beginner? The former. Past beginner? The latter. It's context. The "strange symbols" I only came across when searching for are described as double-struck. I only found that recently. I only found out yesterday they were also called Blackboard, while replying to others here. Difficulty in finding symbol meanings are no way the hard part of maths, though.