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What does $QAQ^{-1}$ actually mean? - Mathematics Stack Exchange 1 $\begingroup$ When one thinks of matrix products like that, it's helpful to remember that matrices, unlike vectors, have two sets of bases: one for the domain and one for the range Thinking of applying a vector on to the right, we get that the transformation "unrotates" the vector, applies the original transformation in the original basis
abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange The main reason that it takes so long to get to $1+1=2$ is that Principia Mathematica starts from almost nothing, and works its way up in very tiny, incremental steps The work of G Peano shows that it's not hard to produce a useful set of axioms that can prove 1+1=2 much more easily than Whitehead and Russell do
How can 1+1=3 be possible? - Mathematics Stack Exchange 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
factorial - Why does 0! = 1? - Mathematics Stack Exchange $\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$ Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately