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Aug
22
comment Missing steps: Show the sum of the first n positive integers is of order $n^2$
@tomi No such assumption is needed. $[n/2]$ means the integer part of $\frac n2$.
Aug
22
comment product of spaces is a manifold. Are the spaces?
Related: Simpler version of dogbone space construction
Aug
20
comment How to convert a decimal to a fraction easily?
There are obviously no 2s nor 5s in the prime factorization of 3760683761.
Aug
18
comment 'normally distributed random numbers' vs 'uniformly distributed random number'?
@marco If you roll even as few as 2 dice and average them, the result is not uniformly distributed. The result is twice as likely to be 3.5 as it is to be 2.
Aug
18
comment Strassen's Algorithm for matrix multiplication
@peter Strassen's algorithm is well-known, and the many people who can answer this question will not need the reminder.
Aug
11
comment What do you call an object that can have duplicate elements?
In computer science it is often called a bag
Aug
10
comment Last digit of a perfect square must be $0, 1, 4, 5, 6,$ or $9$
The unit place of $x^2$ depends only on the unit place of $x$. How many cases are there for the unit place of $x$?
Aug
10
comment Is “smarter than” a transitive relationship?
Yes, but I wanted smarter people to have larger numbers than less smart people, instead of smaller numbers.
Aug
7
comment A proper definition of $i$, the imaginary unit
You left out a crucial step: Why should $(-1, 0)$ be identified with $-1$? The answer is that (a) $(0,0)$ can be identified with $0$ because $(0,0)+(a,b) = (a,b)$ for all $(a,b)$, and $(-1,0) + (1, 0) = (0,0)$.
Aug
7
comment A proper definition of $i$, the imaginary unit
I think Alex means the usual multiplication for complex numbers.
Aug
7
comment A proper definition of $i$, the imaginary unit
I object to your use of the word "the" in "the proper definition". There are several equally good definitions. For example, in algebra we invariably define $i$ as a certain equivalence class of polynomials in a certain ring.
Aug
6
comment Show that $A \lor B ⊢ B \lor A$
It is never a good idea to accuse anyone of downvoting anything, because you do not and cannot know who is really responsible.
Aug
6
comment Show that $A \lor B ⊢ B \lor A$
\land is $\land$
Aug
6
comment Show that $A \lor B ⊢ B \lor A$
Or at least the primitive rules that involve $\lor$.
Aug
6
comment Show that $A \lor B ⊢ B \lor A$
You have an undischarged assumption of $\lnot A$, so this only proves $A\lor B \vdash \lnot A\to (B\lor A)$.
Aug
6
comment What is the group for the following presentation?
Does $(ac)^{n1}$ here mean $(ac)^{n_1}$?
Aug
4
comment Solve the trigonometric equation $\csc^2 \theta= 5 \cot \theta + 7$
$\cot \theta = \frac{\cos \theta}{\sin \theta}$, not $\frac{\sin \theta}{\cos \theta}$.
Aug
2
comment The number $\sum\limits_{n=-\infty}^{\infty} \frac{1}{2^{n^2}}$ is transcendental
Your constant is a Liouville number. “In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence of transcendental numbers for the first time.”
Jul
31
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.
Jul
30
comment Count all possible combinations
Yes, that is correct, it is $20×20= 400$. Wikipedia calls this the Rule of Product or “counting principle>".