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Bookmark or Share- Good book for self study of a First Course in Real AnalysisI think a good first book is 'A First Course in Mathematical Analysis' by David Alexandar Brannan and can suggest it as well as several that have already been mentioned on this page, but this one has the advantage that it was a byproduct of the Open University and is thus totally designed for self-study.
- Connection between cross product and determinantThere certainly is a connection! Other answers have shown that, of course, but it goes a little deeper than that: determinants and cross products are both based on antisymmetric linear combinations of permutations.
- Why have we chosen our number system to be decimal (base 10)?I think the answer here might be, that the guys who thought base 10 was a good idea had the largest sticks. If one trusts the wikipedia, the Babylonians had a base 60 system, which can still be felt today with this "60 minutes in an hour" nonsense, and a (related) base 12 system was widely in use too.
- What does a "half derivative" mean? - Mathematics Stack ExchangeHere's why, lets ask the question not what 1/2 means in therms of children but how it came along. It came along because we wanted to generalize the set of numbers to include stuff in between the integers. It came along for applications besides counting children and is in fact most specifically an "accidental-byproduct" of the existence of division.
- What is the set-theoretic definition of a function?How can we specify the $\mathbb N$-th iteration of power sets of $\mathbb N$ (that is the limit of all finite iterations)? We can define how these things look like, and swipe them all off in one short definition. Not everything is definable, somethings just exist as a byproduct of a definable object (i.e. definable with parameters). $\endgroup$
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