Is Wikipedia a reputable source for Mathematics? I am currently in High School, possibly interested in pursuing a career in Mathematics or the Philosophy/Logic behind Mathematics. I don't have a lot of money for books or videos about Higher Mathematics, but I have been using Wikipedia to learn Maths.
I don't understand why nothing can be as concise and beautiful as Wikipedia. When we learned about functions in school, my teacher took an entire class just to explain them to us. He kept trying to use visuals and all these different tools to explain what a function is, and then, mildly confused, I looked up "function" on Wikipedia, and here is the definition I get:
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
I would much rather use Wikipedia to learn Mathematics, because of how concise it is. Sometimes I don't want to know every single thing about a function, I just want a sufficient definition.
Is there any encyclopedia or book that will have definitions and teach you  Mathematics in this way? I'm not trying to sound egotistic. I am just a very fast learner and I would much rather blaze through a paragraph that explains things very concisely than spend hours learning the same material in different ways. Is Wikipedia good for learning Mathematics, or is there an alternative way to concisely learn what I want to know?
 A: Wikipedia is a good source for reminding yourself of definitions, and is generally accurate. However, learning math from Wikipedia is probably not a very effective strategy because it does not have a "path" for you to take and it is an extremely terse regurgitation of facts.
I would recommend the book "A Transition to Advanced Mathematics". Its pdf is freely available online and it provides a great introduction to proofs and basic set theory as well as some of the other foundational concepts in more advanced math.
A: The others explained quite well how to use wikipedia. Good for you if you can get a good understanding of concepts only from definitions, it means you have good visualisation abilities. High school lessons are indeed full of drawings and examples (in some countries more than others), but the more advanced your classes are, the less explanations you will have. There will always be a point, though, where definitions will not be enough.
PS : I think you would be very interested in metamathematics (look up a little first order logic on wikipedia). 
