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To be completely honest, I find it hard to believe when people claim that the reason they never 'got' mathematics was because of the notation. Actually understa

To be completely honest, I find it hard to believe when people claim that the reason they never 'got' mathematics was because of the notation. Actually understanding the concepts will almost always be significantly harder than understanding notation.

doubleunplussed 6y ago
There is a natural tendency to avoid learning the notation. Even though it would be easy, it goes against our instincts to intentionally go out of our way to look up notation we don't understand. With natural language one often picks up the meaning of new words based on context, after a bit of repetition. So it does not come naturally to people to do otherwise.
- throwaway_pdp09 6y ago
  > to look up notation we don't understand Not so easy. I was trying to find out which of NN and ZZ was what, try searching for those. If you don't know what the signa (summing) sign means, how are you going to find it?
  - doubleunplussed 6y ago
    A quick google revealed this easily. Ctrl-f'ing this article https://en.wikipedia.org/wiki/List_of_mathematical_symbols https://en.wikipedia.org/wiki/List_of_mathematical_symbols for "Sigma" gets you that capital sigma is the summation symbol. ℤ etc are there too though they are admittedly harder to Ctrl-f for. Good luck googling for operators in a programming language as well though. Like with a programming language, for which you might want to skim a tutorial, if you are doing real analysis or whatever is talking about the sets of integers or natural numbers, you might want to skim the opening pages of a textbook or other course. The most common things are usually defined early on, and the less common things are often defined in-text when they are used, e.g "consider the bijective function f: ℤ→ℤ", now you know what f is and just need to google "bijective function". And if you do you'll see the notation about the domain and codomain (which you would also see in the opening chapters of an analysis textbook or lecture notes). I mean, learning how to use a programming language involves having to do some reading too to get to grips with hard-to-google things. Maths is no different.
    - throwaway_pdp09 6y ago
      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.
throwaway_pdp09 6y ago
Notation can be difficult. Given my years with logic I can now read a reasonably complex piece of it and hope to interpret it quite easily if I have some feeling for where the author's going. It does take practice but you need to be exposed to it a fair bit (as when learning a natural language) and have someone to ask, to talk it through with you, until you find your feet. Without some coaching from my uni lecturers at first, and a very good book as well, I probably would have given up.
UK-Al05 6y ago
When I was young, I remember mathematical notation being intimidating when getting started.

doubleunplussed 6y ago

There is a natural tendency to avoid learning the notation. Even though it would be easy, it goes against our instincts to intentionally go out of our way to look up notation we don't understand. With natural language one often picks up the meaning of new words based on context, after a bit of repetition. So it does not come naturally to people to do otherwise.

throwaway_pdp09 6y ago
> to look up notation we don't understand Not so easy. I was trying to find out which of NN and ZZ was what, try searching for those. If you don't know what the signa (summing) sign means, how are you going to find it?
- doubleunplussed 6y ago
  A quick google revealed this easily. Ctrl-f'ing this article https://en.wikipedia.org/wiki/List_of_mathematical_symbols https://en.wikipedia.org/wiki/List_of_mathematical_symbols for "Sigma" gets you that capital sigma is the summation symbol. ℤ etc are there too though they are admittedly harder to Ctrl-f for. Good luck googling for operators in a programming language as well though. Like with a programming language, for which you might want to skim a tutorial, if you are doing real analysis or whatever is talking about the sets of integers or natural numbers, you might want to skim the opening pages of a textbook or other course. The most common things are usually defined early on, and the less common things are often defined in-text when they are used, e.g "consider the bijective function f: ℤ→ℤ", now you know what f is and just need to google "bijective function". And if you do you'll see the notation about the domain and codomain (which you would also see in the opening chapters of an analysis textbook or lecture notes). I mean, learning how to use a programming language involves having to do some reading too to get to grips with hard-to-google things. Maths is no different.
  - throwaway_pdp09 6y ago
    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.

throwaway_pdp09 6y ago

Notation can be difficult. Given my years with logic I can now read a reasonably complex piece of it and hope to interpret it quite easily if I have some feeling for where the author's going. It does take practice but you need to be exposed to it a fair bit (as when learning a natural language) and have someone to ask, to talk it through with you, until you find your feet. Without some coaching from my uni lecturers at first, and a very good book as well, I probably would have given up.

UK-Al05 6y ago

When I was young, I remember mathematical notation being intimidating when getting started.