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14h
comment Count all possible combinations
Yes, that is correct, it is $20×20= 400$. Wikipedia calls this the Rule of Product or “counting principle>".
1d
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 ${\mathfrak c}^{\mathfrak c}$.
1d
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.
2d
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
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
comment Cube root of a fraction
The source is Mary Jane Sterling, U Can: Algebra I for dummies, p. 307.
Jul
25
comment Cube root of a fraction
It says $x=\sqrt[3]{\frac23}$ or $x=\sqrt[3]{-1}$, not that $x$ equals both at the same time.
Jul
21
comment Are there ways to separate the Fibonacci sequence?
He probably doesn't mean $\cup$, because then the answer is trivial.
Jul
20
comment More Symmetric than the symmetric groups?
The question has been corrected so that this answer is no longer pertinent.
Jul
20
comment More Symmetric than the symmetric groups?
I think the question you should be asking is if there's a group of size at most $n!$ that has more subgroups than $S_n$. Comparing a group of size $n$ with $S_n$, which has $n!$ elements, isn't fair.
Jul
20
comment a natural number that is both a perfect square and a perfect cube is a perfect sixth power?
You can show that if $n$ is a perfect cube, then so is $\sqrt n$.
Jul
16
comment Is our Arabic number system based on a geometric design counting corners?
The idea is Hindi, but the numeral forms themselves are from Arabic, just as Latin letter forms are based on Greek and not on Phoenician.
Jul
16
comment Is our Arabic number system based on a geometric design counting corners?
@leox our numerals are from Arabic forms. The Arabic forms are based on earlier Hindi forms.
Jul
16
comment Is our Arabic number system based on a geometric design counting corners?
Short answer: it is not based on that.
Jul
16
comment In a chain of equalities/inequalities, is each line referring to the previous one?
It's conceivable that someone could mean that, and it's not bonkers, but in published mathematical work it never does mean that; it always means $A=B; B\subsetneq C; C=D$.
Jul
15
comment eliminating variable from a pair of trig relations
Next time please try to choose a descriptive title for your post. Do not title it "help me pls".
Jul
15
comment Find numbers $\overline{abcd}$ so that $\overline{abcd}+\overline{bcd}+\overline{cd}+d+1=\overline{dcba}$
You're absolutely right. Fortunately it doesn't otherwise change the discussion. Please feel free to edit the post if you like.
Jul
15
comment Find numbers $\overline{abcd}$ so that $\overline{abcd}+\overline{bcd}+\overline{cd}+d+1=\overline{dcba}$
Incidentally, $15512 + 5512 + 512 + 12 + 2 + 1 = 21551$ and $67967 + 7967 + 967 + 67 + 7 + 1 = 76976$.
Jul
15
comment Find numbers $\overline{abcd}$ so that $\overline{abcd}+\overline{bcd}+\overline{cd}+d+1=\overline{dcba}$
@lulu $\overline{abcd}$ means the number $10^3a+10^2b+10c+d$.
Jul
9
comment Should the empty set be called “half-open”?
So what's your point?