The correct definition of a biproduct is discussed extensively in this blog post.The conditions you write down are morally wrong because they don't guarantee uniqueness up to unique isomorphism, which is something you'd like any universal thing to satisfy.

Yes! In fact, this is a byproduct of what's commonly known as the second fundamental theorem of calculus ...

Here'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.

2023年12月28日 · There 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.

It is not true that a finer cover necessarily contains more open sets than a coarser one. Consider $\Bbb Z$ with the discrete topology: $\mathscr{U}=\{\Bbb Z\}$ is an open cover of $\Bbb Z$ with one member, $\mathscr{V}=\big\{\{n\}:n\in\Bbb Z\big\}$ is an open cover of $\Bbb Z$ with (countably) infinitely many members, yet $\mathscr{V}$ is a refinement of $\mathscr{U}$ and therefore finer than ...

2011年9月6日 · I 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.

2013年10月20日 · The argument itself is the byproduct of my attempts to make sense of the wonderful proof attributed to Landau—which deserves a post of its own here—as presented by Antoine Chambert-Loir on his blog. Although I haven’t encountered it (i.e., the argument below) anywhere else, it’s neither too complicated nor particularly deep, and as such ...

2015年5月18日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

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.