4 ms·

That's a rather long text to say "it's an arbitrary -- and conveniently chosen -- definition of a special case of the power function similar to how 1 is not pri

by quchen 13y ago

That's a rather long text to say "it's an arbitrary -- and conveniently chosen -- definition of a special case of the power function similar to how 1 is not prime". I also think the presentation was chosen poorly: lots of wrong information before the correct approach is presented. Wikipedia is probably a better source here: https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zero https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zer...

ars 13y ago
In no way was wikipedia better, it was confusing and basically incomprehensible unless you already understood the material. His presentation was much better because it leads you to the answer instead of dropping it on you from the sky. (The difference between learning by rote vs learning by understanding.)
- Bahamut 13y ago
  Amusingly, Wikipedia cites this very webpage from the OP.
forrestthewoods 13y ago
I love Wikipedia. It's amazing. It makes the world a better place. I'm a pretty decent programmer. I do video games so I do lots of 3d math. I'd say I'm decent at that as well. I hate Wikipedia for math. Absolutely hate it. Unless you are a mathematician by trade Wikipedia is damn near useless for learning new math concepts. I don't even bother checking it anymore.
- vlasev 13y ago
  I had an idea for a couple of years now of creating a wikipedia-style mathematics textbook that will be crowd-sourced, standardized and cover all of math in a way that's accessible to learn from on your own. It would have a kind of a zoom function where you can expand details on explanations and calculations to a depth that you prefer. Ideally this kind of thing would start off with basic math and get progressively further into mathematics like the roots of a tree.
  - sedeki 13y ago
    I would be really interested in following and/or contributing to this project.
  - marcosdumay 13y ago
    Your "basic" in basic Math means "foundational", or "what we teach to children"?
    - vlasev 13y ago
      That's a good question. In the spirit of making learning easier it would perhaps "start" with what we teach children. However, that might be ultimately misguided because that would just mimic the curriculum and force the whole thing into a box. But then again the math knowledge itself forces a structure on any such textbook because to know A you need to know B, C, D, etc. This is further complicated by the fact that most subjects in math can be approached from multiple equivalent angles. For example, complex analysis can be taught from the complex derivative perspective or from the power series perspective equally well. Ideally the format of the whole thing will allow the student to naturally learn things from the angle they understand better.
  - ivan_ah 13y ago
    That is not a bad idea at all.,, It will be a lot of work but it could be done. Crowd sourcing might lead to the wikipedia-style schizophrenic-author voice of writing, though. See [1] for a prev discussion. Interestingly, if the book is organized so it is aligned to the common core math standard[2], it would make a killing in the US market since current textbooks are so bad. [1] https://news.ycombinator.com/item?id=7456397 https://news.ycombinator.com/item?id=7456397 [2] http://www.corestandards.org/Math/ http://www.corestandards.org/Math/
- deleted 13y ago
  [deleted]
  - scythe 13y ago
    I have also found Wikipedia to be a convenient math reference, but it is not always the "best" that is easily available on the internet. If I'm looking at a topic, it's usually fruitful to Google "introduction to X theory" and go through a few possibilities to find a literature review. Often there is a review which is a good "companion" to the Wikipedia article in terms of explanation, since the style will be different and you get some breadth of perspective. >that that's attributable to math being hard (an easily underestimated property of mathematics)
  - forrestthewoods 13y ago
    I disagree. There are math concepts that I've found impossible to pick up from wikipedia but can easily be learned in 5 minutes by having a conversation with someone who already understands them. Honestly this article in question is a perfect example. I'd wager than almost everyone who reads Hacker News can read the blog post and understand every single step from start to finish. The same can not be said for the Wikipedia article.
    - chunky1994 13y ago
      For questions about mathematical correctness I highly prefer wikipedia. To me it's far more specific and clear, while the original article makes rather short work of proofs. When it comes down to questions that involve first principles, I would much rather have rigor over a less time consuming but potentially wrong understanding of the material, and wikipedia does quite well in providing that rigor.
na85 13y ago
My experience has usually been that Wikipedia is an abysmally bad tool for learning mathematics. The articles seem to be written by someone who has zero clue how to teach the concepts and merely is trying to wow the reader with their proof-writing skills.
- Bahamut 13y ago
  That is because the majority of Wikipedia's math articles are actually from Planet Math, a website full of math knowledge similar to MathWorld that is geared towards mathematicians.
- nzp 13y ago
  That's because Wikipedia isn't a tool to learn mathematics. Wikipedia articles (on anything) are not meant to teach about a subject (in the sense of schooling) but rather to give an exposition of a subject. It is considered to be very bad style on Wikipedia to write articles that try to teach the reader as a textbook or a class would.

by quchen 13y ago

ars 13y ago

In no way was wikipedia better, it was confusing and basically incomprehensible unless you already understood the material. His presentation was much better because it leads you to the answer instead of dropping it on you from the sky. (The difference between learning by rote vs learning by understanding.)

Bahamut 13y ago
Amusingly, Wikipedia cites this very webpage from the OP.

forrestthewoods 13y ago

I love Wikipedia. It's amazing. It makes the world a better place. I'm a pretty decent programmer. I do video games so I do lots of 3d math. I'd say I'm decent at that as well. I hate Wikipedia for math. Absolutely hate it. Unless you are a mathematician by trade Wikipedia is damn near useless for learning new math concepts. I don't even bother checking it anymore.

vlasev 13y ago
I had an idea for a couple of years now of creating a wikipedia-style mathematics textbook that will be crowd-sourced, standardized and cover all of math in a way that's accessible to learn from on your own. It would have a kind of a zoom function where you can expand details on explanations and calculations to a depth that you prefer. Ideally this kind of thing would start off with basic math and get progressively further into mathematics like the roots of a tree.
- sedeki 13y ago
  I would be really interested in following and/or contributing to this project.
- marcosdumay 13y ago
  Your "basic" in basic Math means "foundational", or "what we teach to children"?
  - vlasev 13y ago
    That's a good question. In the spirit of making learning easier it would perhaps "start" with what we teach children. However, that might be ultimately misguided because that would just mimic the curriculum and force the whole thing into a box. But then again the math knowledge itself forces a structure on any such textbook because to know A you need to know B, C, D, etc. This is further complicated by the fact that most subjects in math can be approached from multiple equivalent angles. For example, complex analysis can be taught from the complex derivative perspective or from the power series perspective equally well. Ideally the format of the whole thing will allow the student to naturally learn things from the angle they understand better.
- ivan_ah 13y ago
  That is not a bad idea at all.,, It will be a lot of work but it could be done. Crowd sourcing might lead to the wikipedia-style schizophrenic-author voice of writing, though. See [1] for a prev discussion. Interestingly, if the book is organized so it is aligned to the common core math standard[2], it would make a killing in the US market since current textbooks are so bad. [1] https://news.ycombinator.com/item?id=7456397 https://news.ycombinator.com/item?id=7456397 [2] http://www.corestandards.org/Math/ http://www.corestandards.org/Math/
deleted 13y ago
[deleted]
- scythe 13y ago
  I have also found Wikipedia to be a convenient math reference, but it is not always the "best" that is easily available on the internet. If I'm looking at a topic, it's usually fruitful to Google "introduction to X theory" and go through a few possibilities to find a literature review. Often there is a review which is a good "companion" to the Wikipedia article in terms of explanation, since the style will be different and you get some breadth of perspective. >that that's attributable to math being hard (an easily underestimated property of mathematics)
- forrestthewoods 13y ago
  I disagree. There are math concepts that I've found impossible to pick up from wikipedia but can easily be learned in 5 minutes by having a conversation with someone who already understands them. Honestly this article in question is a perfect example. I'd wager than almost everyone who reads Hacker News can read the blog post and understand every single step from start to finish. The same can not be said for the Wikipedia article.
  - chunky1994 13y ago
    For questions about mathematical correctness I highly prefer wikipedia. To me it's far more specific and clear, while the original article makes rather short work of proofs. When it comes down to questions that involve first principles, I would much rather have rigor over a less time consuming but potentially wrong understanding of the material, and wikipedia does quite well in providing that rigor.

na85 13y ago

My experience has usually been that Wikipedia is an abysmally bad tool for learning mathematics. The articles seem to be written by someone who has zero clue how to teach the concepts and merely is trying to wow the reader with their proof-writing skills.

Bahamut 13y ago
That is because the majority of Wikipedia's math articles are actually from Planet Math, a website full of math knowledge similar to MathWorld that is geared towards mathematicians.
nzp 13y ago
That's because Wikipedia isn't a tool to learn mathematics. Wikipedia articles (on anything) are not meant to teach about a subject (in the sense of schooling) but rather to give an exposition of a subject. It is considered to be very bad style on Wikipedia to write articles that try to teach the reader as a textbook or a class would.