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revised Why this $\sigma \pi \sigma^{-1}$ keeps apearing in my group theory book? (cycle decomposition)
added 12 characters in body
1h
revised Why this $\sigma \pi \sigma^{-1}$ keeps apearing in my group theory book? (cycle decomposition)
added 309 characters in body
1h
answered Why this $\sigma \pi \sigma^{-1}$ keeps apearing in my group theory book? (cycle decomposition)
1d
comment Have I just discovered an easy way to square numbers?
I don't want to run down your discovery, which is legitimate mathematics, and you should be pleased with yourself for discovering it. But it is not publishable anywhere except perhaps on your blog, because it was discovered in prehistoric times.
2d
revised Bogus set theory proof
deleted 6 characters in body; edited tags
2d
revised Count all possible combinations
edited tags
2d
comment Count all possible combinations
Yes, that is correct, it is $20×20= 400$. Wikipedia calls this the Rule of Product or “counting principle>".
2d
revised Digit sum of $n^2$ is 44
8 was missing
2d
revised Digit sum of $n^2$ is 44
edited title
Jul
30
comment “Every function can be represented as a Fourier series”?
A straightforward counting argument shows that most functions cannot be represented as a Fourier series. A Fourier series is determined by a countable family of Fourier coefficients, so the set of such series has cardinality ${\mathfrak c}^{\aleph_0}$, whereas the set of real valued functions defined on some interval has cardinality ${\mathfrak c}^{\mathfrak c}$.
Jul
29
comment Why does our number system have only 10 different symbols?
@InsertPseudonym That book Hagen von Eitzen prepared shows pretty clearly that although different cultures use different bases, the bases are always related to 10; typically if they are not base 10 they are base 20, or an elaboration on base 5, or an elaboration on base 10 like the Babylonians' 60. They are never, for example, base 12 or 8.
Jul
28
revised Examples of mathematical induction
another fun example
Jul
28
comment How similar are pullbacks to products?
I may be mistaken, but I think in English we always call the overcategory a "slice category".
Jul
28
revised Building a box from smaller boxes
added 8 characters in body
Jul
28
answered Building a box from smaller boxes
Jul
28
revised Building a box from smaller boxes
edited tags
Jul
25
revised What is the precise difference between functions and operators?
edited tags
Jul
25
comment Can you help me make sense of this notation?
Related: How does one calculate: $\left(\frac{z}{2!}-\frac{z^3}{4!}+\frac{z^5}{6!}-\cdots\right)^2$
Jul
25
answered Cube root of a fraction
Jul
25
comment Cube root of a fraction
The source is Mary Jane Sterling, U Can: Algebra I for dummies, p. 307.